Compute Distance To:
 Documents Indexed: 154 Publications since 1966, including 6 Books 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 58 Co-Authors with 119 Joint Publications 2,094 Co-Co-Authors
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### Co-Authors

 37 single-authored 41 Ebeling, Wolfgang 28 Delgado, Felix 27 Campillo, Antonio 22 Melle-Hernández, Alejandro 21 Luengo, Ignacio 9 Varchenko, Alexander Nikolaevich 6 Arnol’d, Vladimir Igorevich 4 Ilyashenko, Yulij Sergeevich 3 Lando, Sergei K. 3 Natanzon, Sergei M. 3 Tsfasman, Michael A. 2 Nekhoroshev, Nikolaĭ Nikolaevich 2 Rauch, A.-M. Ya. 2 Rybnikov, Leonid Grigor’evich 2 Vasil’ev, Viktor Anatol’evich 1 Agrachev, Andreĭ Aleksandrovich 1 Aliev, Nihan A. 1 Anosov, Dmitriĭ Viktorovich 1 Arzhantsev, Ivan Vladimirovich 1 Bogaevskij, Il’ya Aleksandrovich 1 Bortakovskii, A. S. 1 Budak, A. B. 1 Bukhshtaber, Viktor Matveevich 1 Chubarikov, Vladimir Nikolaevich 1 Costa Gonzáles, Antonio Félix 1 Davydov, Alekseĭ Aleksandrovich 1 Duzhin, Fedor S. 1 Etingof, Pavel Il’ich 1 Gorsky, Eugene 1 Goryunov, Victor V. 1 Guliyeva, Arzu M. 1 Hernando, Fernando 1 Kazaryan, Maxim Eduardovich 1 Khanin, Konstantin M. 1 Khovanskiĭ, Askold Georgievich 1 Kozlov, Valeriĭ Vasil’evich 1 Krichever, Igor’ Moiseevich 1 Loktev, Sergey A. 1 Luengo, A. I. 1 Mamedova, F. I. 1 Manin, Yuri Ivanovich 1 Nadirashvili, Nikolai S. 1 Nogin, Dmitry Yu. 1 Novikov, Sergeĭ Petrovich 1 Orlov, Dmitri O. 1 Porteous, Hugh L. 1 Rybakov, Sergeĭ Yur’evich 1 Schwarzman, Ossip 1 Seade, Jose Antonio 1 Sedykh, Vyacheslav Dmitrievich 1 Shlosman, Senya B. 1 Siersma, Dirk 1 Sinaĭ, Yakov Grigor’evich 1 Sosinskiĭ, Alekseĭ Bronislavovich 1 Takahashi, Atsushi 1 Timashev, Dmitri A. 1 Treshchev, Dmitriĭ Valer’evich 1 Zarodov, V. R. 1 Zykin, A. I.
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### Serials

 20 Functional Analysis and its Applications 10 Russian Mathematical Surveys 10 Moscow Mathematical Journal 5 Proceedings of the Steklov Institute of Mathematics 4 Bulletin of the London Mathematical Society 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Journal of Geometry and Physics 3 Funktsional’nyĭ Analiz i ego Prilozheniya 3 Mathematische Zeitschrift 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 International Journal of Mathematics 3 Journal of Mathematical Sciences (New York) 3 Revista Matemática Complutense 3 Journal of Singularities 2 Mathematical Notes 2 Teoriya Veroyatnosteĭ i eë Primeneniya 2 Commentarii Mathematici Helvetici 2 Mathematische Nachrichten 2 Monatshefte für Mathematik 2 St. Petersburg Mathematical Journal 2 Mathematical Research Letters 2 Monographs in Mathematics 2 Azerbaijan Journal of Mathematics 2 Modern Birkhäuser Classics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Matematicheskie Zametki 1 Arkiv för Matematik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Geometriae Dedicata 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematics of the USSR. Izvestiya 1 Michigan Mathematical Journal 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Topology and its Applications 1 IMRN. International Mathematics Research Notices 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Selecta Mathematica. New Series 1 Bulletin des Sciences Mathématiques 1 Documenta Mathematica 1 European Mathematical Society Newsletter 1 Doklady Mathematics 1 Advances in Theoretical and Mathematical Physics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of Algebra and its Applications 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Pure and Applied Mathematics Quarterly 1 Functional Analysis and Other Mathematics 1 TWMS Journal of Pure and Applied Mathematics 1 Arnold Mathematical Journal 1 European Journal of Mathematics
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### Fields

 91 Several complex variables and analytic spaces (32-XX) 87 Algebraic geometry (14-XX) 40 Manifolds and cell complexes (57-XX) 36 Global analysis, analysis on manifolds (58-XX) 13 Algebraic topology (55-XX) 12 Commutative algebra (13-XX) 9 Associative rings and algebras (16-XX) 8 $$K$$-theory (19-XX) 7 History and biography (01-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Category theory; homological algebra (18-XX) 3 Quantum theory (81-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

110 Publications have been cited 1,063 times in 725 Documents Cited by Year
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1985
Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1988
Intersection matrices for certain singularities of functions of two variables. Zbl 0304.14009
1974
The monodromy groups of isolated singularities of hypersurfaces. Zbl 0379.32013
1977
The Alexander polynomial of a plane curve singularity via the ring of functions on it. Zbl 1028.32013
2003
A power structure over the Grothendieck ring of varieties. Zbl 1063.14026
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2004
Poincaré series of a rational surface singularity. Zbl 1060.14054
2004
Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. Zbl 1122.14003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
Multi-index filtrations and generalized Poincaré series. Zbl 1111.14020
2007
The Alexander polynomial of a plane curve singularity and integrals with respect to the Euler characteristic. Zbl 1056.14035
2003
On indices of 1-forms on determinantal singularities. Zbl 1202.32023
2009
Universal abelian covers of rational surface singularities and multi-index filtrations. Zbl 1156.14317
2008
On generators of the semigroup of a plane curve singularity. Zbl 0974.14020
1999
Dynkin diagrams for singularities of functions of two variables. Zbl 0309.14006
1974
Poincaré series for several plane divisorial valuations. Zbl 1083.14502
2003
Radial index and Euler obstruction of a 1-form on a singular variety. Zbl 1110.14004
2005
Zeta functions for germs of meromorphic functions, and Newton diagrams. Zbl 0933.32003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1998
On the monodromy of a plane curve singularity and the Poincaré series of its ring of functions. Zbl 0967.14017
1999
Partial resolutions and the zeta-function of a singularity. Zbl 0901.32024
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1997
Saito duality between Burnside rings for invertible polynomials. Zbl 1298.32017
2012
Homological index for 1-forms and a Milnor number for isolated singularities. Zbl 1065.14003
2004
Indices of 1-forms on an isolated complete intersection singularity. Zbl 1039.32033
2003
On the index of a vector field at an isolated singularity. Zbl 0942.57024
1999
Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity. Zbl 1046.32007
2000
Integration with respect to the Euler characteristic and its applications. Zbl 1228.14005
2010
Singularities of differentiable mappings. Classification of critical points, caustics and wave fronts. (Osobennosti differentsiruemykh otobrazhenij. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov). Zbl 0513.58001
Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M.
1982
The Alexander polynomial of plane curve singularities and rings of functions on curves. Zbl 0976.32017
1999
Equivariant Poincaré series of filtrations. Zbl 1276.14005
2013
Indices of vector fields and 1-forms on singular varieties. Zbl 1124.32012
2006
Singularities of differentiable mappings. Monodromy and asymptotics of integrals. (Osobennosti differentsiruemykh otobrazhenij. Monodromiya i asimptotiki integralov). Zbl 0545.58001
Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M.
1984
Verlinde algebras and the intersection form on vanishing cycles. Zbl 0911.32044
1997
On Poincaré series of filtrations on equivariant functions of two variables. Zbl 1131.14007
2007
Orbifold Euler characteristics for dual invertible polynomials. Zbl 1319.14046
2012
On the power structure over the Grothendieck ring of varieties and its applications. Zbl 1222.14007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2007
The problem of choice and the optimal stopping rule for a sequence of independent trails. Zbl 0203.20405
1966
An equivariant Poincaré series of filtrations and monodromy zeta functions. Zbl 1327.14019
2015
Topology of meromorphic germs and its applications. Zbl 0972.32022
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2000
Singularities of type $$A_k$$ on plane curves of a chosen degree. Zbl 0980.32008
Gusein-Zade, S. M.; Nekhoroshev, N. N.
2000
The Poincaré series of divisorial valuations in the plane defines the topology of the set of divisors. Zbl 1203.14031
2010
Equivariant analogues of the Euler characteristic and Macdonald type equations. Zbl 1376.57039
2017
Integrals with respect to the Euler characteristic over spaces of functions and the Alexander polynomial. Zbl 1030.32021
2002
Equivariant indices of vector fields and 1-forms. Zbl 1336.14007
2015
Orbifold E-functions of dual invertible polynomials. Zbl 1379.32025
Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi
2016
Poincaré series of curves on rational surface singularities. Zbl 1075.14024
2005
An equivariant version of the monodromy zeta function. Zbl 1156.32016
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2008
On the pre-$$\lambda$$-ring structure on the Grothendieck ring of stacks and the power structures over it. Zbl 1272.14006
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2013
Poincaré series of collections of plane valuations. Zbl 1213.32013
2010
Indices of vector fields or 1-forms and characteristic numbers. Zbl 1086.32025
2005
Dual invertible polynomials with permutation symmetries and the orbifold Euler characteristic. Zbl 1440.14187
2020
Orbifold zeta functions for dual invertible polynomials. Zbl 1360.14107
2017
Bifurcations and topology of meromorphic germs. Zbl 0991.32019
Gusein-Zade, Sabir; Luengo, Ignacio; Hernández, Alejandro Melle
2001
Quadratic forms for a 1-form on an isolated complete intersection singularity. Zbl 1089.32018
2006
On a game connected with a Wiener process. Zbl 0191.49702
1969
The extended semigroup of a plane curve singularity. Zbl 1048.58027
1998
On the zeta-function of a polynomial at infinity. Zbl 0970.32015
Gusein-Zade, Sabir M.; Luengo, Ignacio; Melle-Hernández, Alejandro
2000
Higher order generalized Euler characteristics and generating series. Zbl 1320.32029
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
Index of a singular point of a gradient vector field. Zbl 0555.32006
1984
Monodromies and Poincaré series of quasihomogeneous complete intersections. Zbl 1070.14004
2004
On the existence of deformations without critical points (the Teissier problem for functions of two variables). Zbl 0911.32046
1997
Grothendieck ring of varieties with actions of finite groups. Zbl 1454.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2019
On the orbifold Euler characteristics of dual invertible polynomials with non-abelian symmetry groups. Zbl 1455.14078
2020
Equivariant versions of higher order orbifold Euler characteristics. Zbl 1382.55004
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2016
On the topological type of a set of plane valuations with symmetries. Zbl 1397.13009
2017
Hilbert function, generalized Poincaré series and topology of plane valuations. Zbl 1325.14010
2014
On adjacencies of singularities $$A_ k$$ to points of the $$\mu =const$$ stratum of a singularity. Zbl 0555.32008
Gusejn-Zade, S. M.; Nekhoroshev, N. N.
1983
Poincaré series and zeta function of the monodromy of a quasihomogeneous singularity. Zbl 1056.14003
2002
On the number of topological types of plane curves. Zbl 0915.57004
Gusein-Zade, S. M.; Duzhin, F. S.
1998
On the index of a holomorphic $$1$$-form on an isolated complete intersection singularity. Zbl 1086.32501
2001
Equivariant Poincaré series of filtrations and topology. Zbl 1317.14006
2014
Integration over spaces of nonparametrized arcs and motivic versions of the monodromy zeta function. Zbl 1350.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
On generating series of classes of equivariant Hilbert schemes of fat points. Zbl 1206.14014
Gusein-Zade, S.; Luengo, I.; Melle-Hernández, A.
2010
Orbifold Milnor lattice and orbifold intersection form. Zbl 1393.14056
2018
The universal Euler characteristic of $$V$$-manifolds. Zbl 1423.57042
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2018
Method of real morsifications for complete intersection singularities. Zbl 0829.14022
1994
Chern obstructions for collections of 1-forms on singular varieties. Zbl 1130.32011
2007
Coxeter-Dynkin diagrams of the complete intersection singularities $$Z_ 9$$ and $$Z_{10}$$. Zbl 0834.14002
1995
Klein foams as families of real forms of Riemann surfaces. Zbl 1366.81270
Gusein-Zade, Sabir M.; Natanzon, Sergey M.
2017
Higher-order spectra, equivariant Hodge-Deligne polynomials, and Macdonald-type equations. Zbl 1454.57020
2017
Multi-variable Poincaré series associated with Newton diagrams. Zbl 1302.32025
2010
On divisorial filtrations associated with Newton diagrams. Zbl 1292.32008
2011
On singularities from which an $$A_ 1$$ can be split off. Zbl 0793.32013
1993
A version of the Berglund-Hübsch-Henningson duality with non-abelian groups. Zbl 1479.14048
2021
Number of critical points for a quasiperiodic potential. Zbl 0711.58007
1989
On singularities admitting perturbations with a small number of critical values. Zbl 0626.32025
1987
On an equivariant version of the zeta function of a transformation. Zbl 1325.32030
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
On the action of a circle on manifolds. Zbl 0235.57014
1972
U-actions of a circle and fixed points. Zbl 0248.57026
1972
Equivariant Poincaré series and topology of valuations. Zbl 1431.14004
2016
On indices of meromorphic 1-forms. Zbl 1060.32013
2004
On the zeta functions of a meromorphic germ in two variables. Zbl 1077.14039
2004
On the topology of quasiperiodic functions. Zbl 0959.58048
1999
Monodromiegruppen isolierter Singularitäten von Hyperflächen. Zbl 0363.32010
1977
On the monodromy at infinity of a plane curve and the Poincaré series of its coordinate ring. Zbl 1005.14012
1999
The Arf-invariant and the Arnold invariants of plane curves. Zbl 1076.57500
Gusein-Zade, S. M.; Natanzon, S. M.
1997
Dynkin diagrams of some complete intersections and real morsifications. Zbl 0882.32017
1995
On atypical values and local monodromies of meromorphic functions. Zbl 0990.32007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1999
Distinguished bases of simple singularities. Zbl 0484.32002
1981
Alexander polynomials and Poincaré series of sets of ideals. Zbl 1271.32032
2011
A version of the Berglund-Hübsch-Henningson duality with non-abelian groups. Zbl 1479.14048
2021
Dual invertible polynomials with permutation symmetries and the orbifold Euler characteristic. Zbl 1440.14187
2020
On the orbifold Euler characteristics of dual invertible polynomials with non-abelian symmetry groups. Zbl 1455.14078
2020
Grothendieck ring of varieties with actions of finite groups. Zbl 1454.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2019
Orbifold Milnor lattice and orbifold intersection form. Zbl 1393.14056
2018
The universal Euler characteristic of $$V$$-manifolds. Zbl 1423.57042
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2018
Power structure over the Grothendieck ring of maps. Zbl 1423.14061
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2018
Equivariant analogues of the Euler characteristic and Macdonald type equations. Zbl 1376.57039
2017
Orbifold zeta functions for dual invertible polynomials. Zbl 1360.14107
2017
On the topological type of a set of plane valuations with symmetries. Zbl 1397.13009
2017
Klein foams as families of real forms of Riemann surfaces. Zbl 1366.81270
Gusein-Zade, Sabir M.; Natanzon, Sergey M.
2017
Higher-order spectra, equivariant Hodge-Deligne polynomials, and Macdonald-type equations. Zbl 1454.57020
2017
On equivariant indices of 1-forms on varieties. Zbl 1398.32036
Gusein-Zade, S. M.; Mamedova, F. I.
2017
An equivariant version of the Euler obstruction. Zbl 1380.32011
2017
Orbifold E-functions of dual invertible polynomials. Zbl 1379.32025
Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi
2016
Equivariant versions of higher order orbifold Euler characteristics. Zbl 1382.55004
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2016
Equivariant Poincaré series and topology of valuations. Zbl 1431.14004
2016
An equivariant Poincaré series of filtrations and monodromy zeta functions. Zbl 1327.14019
2015
Equivariant indices of vector fields and 1-forms. Zbl 1336.14007
2015
Higher order generalized Euler characteristics and generating series. Zbl 1320.32029
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
On an equivariant version of the zeta function of a transformation. Zbl 1325.32030
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
On Poincaré series of filtrations. Zbl 1406.13021
2015
Hilbert function, generalized Poincaré series and topology of plane valuations. Zbl 1325.14010
2014
Equivariant Poincaré series of filtrations and topology. Zbl 1317.14006
2014
Equivariant Poincaré series of filtrations. Zbl 1276.14005
2013
On the pre-$$\lambda$$-ring structure on the Grothendieck ring of stacks and the power structures over it. Zbl 1272.14006
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2013
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Saito duality between Burnside rings for invertible polynomials. Zbl 1298.32017
2012
Orbifold Euler characteristics for dual invertible polynomials. Zbl 1319.14046
2012
On a Newton filtration for functions on a curve singularity. Zbl 1292.32009
2012
Equivariant Poincaré series and monodromy zeta functions of quasihomogeneous polynomials. Zbl 1255.32013
2012
On divisorial filtrations associated with Newton diagrams. Zbl 1292.32008
2011
Alexander polynomials and Poincaré series of sets of ideals. Zbl 1271.32032
2011
Klein foams. Zbl 1268.14027
Costas, Antonio F.; Gusein-Zade, Sabir M.; Natanzon, Sergey M.
2011
Monodromy of dual invertible polynomials. Zbl 1257.32028
2011
Integration with respect to the Euler characteristic and its applications. Zbl 1228.14005
2010
The Poincaré series of divisorial valuations in the plane defines the topology of the set of divisors. Zbl 1203.14031
2010
Poincaré series of collections of plane valuations. Zbl 1213.32013
2010
On generating series of classes of equivariant Hilbert schemes of fat points. Zbl 1206.14014
Gusein-Zade, S.; Luengo, I.; Melle-Hernández, A.
2010
Multi-variable Poincaré series associated with Newton diagrams. Zbl 1302.32025
2010
On indices of 1-forms on determinantal singularities. Zbl 1202.32023
2009
Universal abelian covers of rational surface singularities and multi-index filtrations. Zbl 1156.14317
2008
An equivariant version of the monodromy zeta function. Zbl 1156.32016
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2008
Multi-index filtrations and generalized Poincaré series. Zbl 1111.14020
2007
On Poincaré series of filtrations on equivariant functions of two variables. Zbl 1131.14007
2007
On the power structure over the Grothendieck ring of varieties and its applications. Zbl 1222.14007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2007
Chern obstructions for collections of 1-forms on singular varieties. Zbl 1130.32011
2007
Lectures on monodromy. Zbl 1135.32029
2007
Deformations of polynomials and their zeta-functions. Zbl 1194.32017
2007
Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. Zbl 1122.14003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
Indices of vector fields and 1-forms on singular varieties. Zbl 1124.32012
2006
Quadratic forms for a 1-form on an isolated complete intersection singularity. Zbl 1089.32018
2006
Integration over spaces of nonparametrized arcs and motivic versions of the monodromy zeta function. Zbl 1350.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
Radial index and Euler obstruction of a 1-form on a singular variety. Zbl 1110.14004
2005
Poincaré series of curves on rational surface singularities. Zbl 1075.14024
2005
Indices of vector fields or 1-forms and characteristic numbers. Zbl 1086.32025
2005
A power structure over the Grothendieck ring of varieties. Zbl 1063.14026
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2004
Poincaré series of a rational surface singularity. Zbl 1060.14054
2004
Homological index for 1-forms and a Milnor number for isolated singularities. Zbl 1065.14003
2004
Monodromies and Poincaré series of quasihomogeneous complete intersections. Zbl 1070.14004
2004
On indices of meromorphic 1-forms. Zbl 1060.32013
2004
On the zeta functions of a meromorphic germ in two variables. Zbl 1077.14039
2004
The Alexander polynomial of a plane curve singularity via the ring of functions on it. Zbl 1028.32013
2003
The Alexander polynomial of a plane curve singularity and integrals with respect to the Euler characteristic. Zbl 1056.14035
2003
Poincaré series for several plane divisorial valuations. Zbl 1083.14502
2003
Indices of 1-forms on an isolated complete intersection singularity. Zbl 1039.32033
2003
Integrals with respect to the Euler characteristic over spaces of functions and the Alexander polynomial. Zbl 1030.32021
2002
Poincaré series and zeta function of the monodromy of a quasihomogeneous singularity. Zbl 1056.14003
2002
Bifurcations and topology of meromorphic germs. Zbl 0991.32019
Gusein-Zade, Sabir; Luengo, Ignacio; Hernández, Alejandro Melle
2001
On the index of a holomorphic $$1$$-form on an isolated complete intersection singularity. Zbl 1086.32501
2001
Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity. Zbl 1046.32007
2000
Topology of meromorphic germs and its applications. Zbl 0972.32022
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2000
Singularities of type $$A_k$$ on plane curves of a chosen degree. Zbl 0980.32008
Gusein-Zade, S. M.; Nekhoroshev, N. N.
2000
On the zeta-function of a polynomial at infinity. Zbl 0970.32015
Gusein-Zade, Sabir M.; Luengo, Ignacio; Melle-Hernández, Alejandro
2000
On generators of the semigroup of a plane curve singularity. Zbl 0974.14020
1999
On the monodromy of a plane curve singularity and the Poincaré series of its ring of functions. Zbl 0967.14017
1999
On the index of a vector field at an isolated singularity. Zbl 0942.57024
1999
The Alexander polynomial of plane curve singularities and rings of functions on curves. Zbl 0976.32017
1999
On the topology of quasiperiodic functions. Zbl 0959.58048
1999
On the monodromy at infinity of a plane curve and the Poincaré series of its coordinate ring. Zbl 1005.14012
1999
On atypical values and local monodromies of meromorphic functions. Zbl 0990.32007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1999
Zeta functions for germs of meromorphic functions, and Newton diagrams. Zbl 0933.32003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1998
The extended semigroup of a plane curve singularity. Zbl 1048.58027
1998
On the number of topological types of plane curves. Zbl 0915.57004
Gusein-Zade, S. M.; Duzhin, F. S.
1998
Partial resolutions and the zeta-function of a singularity. Zbl 0901.32024
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1997
Verlinde algebras and the intersection form on vanishing cycles. Zbl 0911.32044
1997
On the existence of deformations without critical points (the Teissier problem for functions of two variables). Zbl 0911.32046
1997
The Arf-invariant and the Arnold invariants of plane curves. Zbl 1076.57500
Gusein-Zade, S. M.; Natanzon, S. M.
1997
Coxeter-Dynkin diagrams of the complete intersection singularities $$Z_ 9$$ and $$Z_{10}$$. Zbl 0834.14002
1995
Dynkin diagrams of some complete intersections and real morsifications. Zbl 0882.32017
1995
Method of real morsifications for complete intersection singularities. Zbl 0829.14022
1994
On singularities from which an $$A_ 1$$ can be split off. Zbl 0793.32013
1993
Number of critical points for a quasiperiodic potential. Zbl 0711.58007
1989
Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002
Arnol&rsquo;d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1988
On singularities admitting perturbations with a small number of critical values. Zbl 0626.32025
1987
Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001
Arnol&rsquo;d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1985
Singularities of differentiable mappings. Monodromy and asymptotics of integrals. (Osobennosti differentsiruemykh otobrazhenij. Monodromiya i asimptotiki integralov). Zbl 0545.58001
Arnol&rsquo;d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M.
1984
Index of a singular point of a gradient vector field. Zbl 0555.32006
1984
On adjacencies of singularities $$A_ k$$ to points of the $$\mu =const$$ stratum of a singularity. Zbl 0555.32008
Gusejn-Zade, S. M.; Nekhoroshev, N. N.
1983
...and 10 more Documents
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### Cited by 809 Authors

 52 Gusein-Zade, Sabir M. 25 Ebeling, Wolfgang 16 Delgado, Felix 16 Némethi, András 14 Campillo, Antonio 12 Luengo, Ignacio 12 Melle-Hernández, Alejandro 10 Moyano Fernández, Julio José 9 Janeczko, Stanisław 9 Soares Ruas, Maria Aparecida 8 Vasil’ev, Viktor Anatol’evich 7 Izumiya, Shyuichi 7 Milanov, Todor E. 6 Bivià-Ausina, Carles 6 Greenblatt, Michael 6 Martín-Morales, Jorge 6 Nagy, János 6 Novikov, Dmitry 6 Seade, Jose Antonio 6 Takahashi, Atsushi 5 Albeverio, Sergio A. 5 Borodzik, Maciej 5 Davydov, Alekseĭ Aleksandrovich 5 de Góes Grulha, Nivaldo jun. 5 Dimca, Alexandru 5 Gorsky, Eugene 5 Goryunov, Victor V. 5 Ikromov, Isroil A. 5 László, Tamás 5 Maxim, Laurentiu G. 5 Shen, Yefeng 5 Siersma, Dirk 5 Takeuchi, Kiyoshi 5 Yakovenko, Sergei 5 Yamada, Yuichi 4 Astashov, Evgeniĭ Aleksandrovich 4 Esterov, Alexander I. 4 Galindo Pastor, Carlos 4 Hertling, Claus 4 Il’yuta, G. G. 4 Kamimoto, Joe 4 Monserrat, Francisco 4 Movasati, Hossein 4 Ricolfi, Andrea T. 4 Schürmann, Jörg 4 Shustin, Eugenii Isaakovich 4 Szendrői, Balázs 4 Varchenko, Alexander Nikolaevich 4 Veys, Willem 4 Zakalyukin, Vladimir M. 4 Zuber, Jean-Bernard 3 Allcock, Daniel Jonathan 3 Arnol’d, Vladimir Igorevich 3 Baryshnikov, Yuliy M. 3 Basalaev, Alexey 3 Binyamini, Gal 3 Challapa, Lizandro Sanchez 3 Chmutov, Sergei V. 3 D’Anna, Marco 3 Dubrovin, Boris Anatol’evich 3 Dunne, Gerald V. 3 Dutertre, Nicolas 3 Gaffney, Terence 3 Gómez-Mont, Xavier 3 Greuel, Gert-Martin 3 Hernando, Fernando 3 Ishikawa, Goo 3 Laza, Radu 3 Manh, Hy Duc 3 Mardešić, Pavao 3 Mazzucchi, Sonia 3 Micale, Vincenzo 3 Morrison, Andrew 3 Nakamura, Yayoi 3 Natanzon, Sergei M. 3 Nose, Toshihiro 3 Nuño-Ballesteros, Juan José 3 Proskurnin, Ivan Andreevich 3 Reeve, Graham Mark 3 Ruan, Yongbin 3 Sedykh, Vyacheslav Dmitrievich 3 Shende, Vivek Vijay 3 Villa, Manuel González 3 Weber, Andrzej 3 Zach, Matthias 3 Żołądek, Henryk 2 Aazami, Amir Babak 2 Abiev, Nurlan Abievich 2 A’Campo, Norbert 2 Aleksandrov, Aleksandr Grigor’evich 2 Alharbi, Fawaz 2 Ardentov, Andrei A. 2 Barbero-Liñán, María 2 Belavin, Aleksandr Abramovich 2 Bryan, Jim 2 Carlson, James A. 2 Ceresole, Anna 2 Chen, Hao 2 Chiodo, Alessandro 2 Cogolludo Agustín, José Ignacio ...and 709 more Authors
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### Cited in 200 Serials

 36 Functional Analysis and its Applications 23 Advances in Mathematics 19 Proceedings of the Steklov Institute of Mathematics 18 Mathematische Zeitschrift 17 Journal of Mathematical Sciences (New York) 16 Journal of Geometry and Physics 16 Annales de l’Institut Fourier 16 Duke Mathematical Journal 16 Topology and its Applications 13 Transactions of the American Mathematical Society 12 Communications in Mathematical Physics 12 Mathematical Notes 12 Journal of High Energy Physics 11 Mathematische Annalen 10 Journal of Differential Equations 10 Manuscripta Mathematica 10 Revista Matemática Complutense 9 Inventiones Mathematicae 9 Journal of Algebra 9 Bulletin of the Brazilian Mathematical Society. New Series 9 Arnold Mathematical Journal 8 Israel Journal of Mathematics 8 Compositio Mathematica 8 Journal of Dynamical and Control Systems 8 Journal of Singularities 7 Journal of Mathematical Physics 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Nuclear Physics. B 7 Selecta Mathematica. New Series 7 Bulletin des Sciences Mathématiques 7 Geometry & Topology 6 Moscow University Mathematics Bulletin 6 Theoretical and Mathematical Physics 6 Journal of Pure and Applied Algebra 6 Journal of Algebraic Geometry 6 Algebraic & Geometric Topology 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Journal of Mathematical Analysis and Applications 5 Geometriae Dedicata 5 Journal of the Mathematical Society of Japan 5 Michigan Mathematical Journal 5 Monatshefte für Mathematik 5 Indagationes Mathematicae. New Series 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Russian Journal of Mathematical Physics 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Differential Geometry and its Applications 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 St. Petersburg Mathematical Journal 4 Doklady Mathematics 4 Annals of Mathematics. Second Series 4 Regular and Chaotic Dynamics 3 Archive for Rational Mechanics and Analysis 3 Communications in Algebra 3 Letters in Mathematical Physics 3 Nonlinearity 3 Rocky Mountain Journal of Mathematics 3 Reviews in Mathematical Physics 3 Bulletin of the London Mathematical Society 3 Osaka Journal of Mathematics 3 Proceedings of the American Mathematical Society 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Tôhoku Mathematical Journal. Second Series 3 Physica D 3 Journal of Symbolic Computation 3 Revista Matemática Iberoamericana 3 International Journal of Mathematics 3 Journal of Knot Theory and its Ramifications 3 Izvestiya: Mathematics 3 The Journal of Fourier Analysis and Applications 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Algebra and its Applications 3 Journal de l’École Polytechnique – Mathématiques 2 International Journal of Modern Physics A 2 Journal of Statistical Physics 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Demonstratio Mathematica 2 Glasgow Mathematical Journal 2 Journal of Combinatorial Theory. Series A 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Tokyo Journal of Mathematics 2 Advances in Applied Mathematics 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Discrete & Computational Geometry 2 Computational Mathematics and Mathematical Physics 2 Applicable Algebra in Engineering, Communication and Computing 2 Sbornik: Mathematics 2 Qualitative Theory of Dynamical Systems 2 Moscow Mathematical Journal 2 Mediterranean Journal of Mathematics 2 Functional Analysis and Other Mathematics 2 Analysis and Mathematical Physics 2 European Journal of Mathematics 1 Discrete Applied Mathematics 1 General Relativity and Gravitation 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique ...and 100 more Serials
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### Cited in 57 Fields

 325 Algebraic geometry (14-XX) 243 Several complex variables and analytic spaces (32-XX) 119 Global analysis, analysis on manifolds (58-XX) 112 Manifolds and cell complexes (57-XX) 96 Differential geometry (53-XX) 67 Dynamical systems and ergodic theory (37-XX) 50 Quantum theory (81-XX) 44 Ordinary differential equations (34-XX) 42 Commutative algebra (13-XX) 40 Partial differential equations (35-XX) 30 Group theory and generalizations (20-XX) 23 Algebraic topology (55-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 19 Associative rings and algebras (16-XX) 17 Number theory (11-XX) 16 Combinatorics (05-XX) 16 Nonassociative rings and algebras (17-XX) 15 Statistical mechanics, structure of matter (82-XX) 13 Systems theory; control (93-XX) 11 Category theory; homological algebra (18-XX) 11 Functions of a complex variable (30-XX) 11 Probability theory and stochastic processes (60-XX) 11 Optics, electromagnetic theory (78-XX) 11 Relativity and gravitational theory (83-XX) 10 Operator theory (47-XX) 10 Mechanics of particles and systems (70-XX) 9 Real functions (26-XX) 9 Measure and integration (28-XX) 9 Convex and discrete geometry (52-XX) 7 $$K$$-theory (19-XX) 7 Approximations and expansions (41-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Numerical analysis (65-XX) 7 Fluid mechanics (76-XX) 6 Mechanics of deformable solids (74-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Topological groups, Lie groups (22-XX) 5 Integral transforms, operational calculus (44-XX) 5 Geometry (51-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Mathematical logic and foundations (03-XX) 4 Field theory and polynomials (12-XX) 4 Operations research, mathematical programming (90-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Biology and other natural sciences (92-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)

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