Stevens, Jan Conjectures on stably Newton degenerate singularities. (English) Zbl 1484.14005 Arnold Math. J. 7, No. 3, 441-465 (2021). Reviewer: Tadeusz Krasiński (Łódź) MSC: 14B05 32S05 14M25 PDFBibTeX XMLCite \textit{J. Stevens}, Arnold Math. J. 7, No. 3, 441--465 (2021; Zbl 1484.14005) Full Text: DOI arXiv
Douai, Antoine Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials. (English) Zbl 1500.52006 J. Algebr. Comb. 54, No. 3, 719-732 (2021). Reviewer: Kunal Dutta (Warsaw) MSC: 52B20 05A15 32S40 14J33 14M25 PDFBibTeX XMLCite \textit{A. Douai}, J. Algebr. Comb. 54, No. 3, 719--732 (2021; Zbl 1500.52006) Full Text: DOI arXiv
Mondal, Pinaki How many zeroes? Counting solutions of systems of polynomials via toric geometry at infinity. (English) Zbl 1483.13001 CMS/CAIMS Books in Mathematics 2. Cham: Springer (ISBN 978-3-030-75173-9/hbk; 978-3-030-75174-6/ebook). xv, 352 p. (2021). Reviewer: Felipe Zaldívar (Ciudad de México) MSC: 13-02 14-02 14M25 52A39 52B20 PDFBibTeX XMLCite \textit{P. Mondal}, How many zeroes? Counting solutions of systems of polynomials via toric geometry at infinity. Cham: Springer (2021; Zbl 1483.13001) Full Text: DOI
Eyral, Christophe; Oleksik, Grzegorz; Różycki, Adam Lê numbers and Newton diagram. (English) Zbl 1457.32078 Adv. Math. 376, Article ID 107441, 22 p. (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 32S25 14J17 14J70 PDFBibTeX XMLCite \textit{C. Eyral} et al., Adv. Math. 376, Article ID 107441, 22 p. (2021; Zbl 1457.32078) Full Text: DOI arXiv
Brzostowski, Szymon; Krasiński, Tadeusz; Walewska, Justyna Arnold’s problem on monotonicity of the Newton number for surface singularities. (English) Zbl 1437.32005 J. Math. Soc. Japan 71, No. 4, 1257-1268 (2019). Reviewer: Ahmed Lesfari (El Jadida) MSC: 32S25 14B05 14J17 PDFBibTeX XMLCite \textit{S. Brzostowski} et al., J. Math. Soc. Japan 71, No. 4, 1257--1268 (2019; Zbl 1437.32005) Full Text: DOI arXiv Euclid
Takahashi, Takuhiro A note on tropical curves and the Newton diagrams of plane curve singularities. (English) Zbl 1437.14068 Tokyo J. Math. 42, No. 1, 51-61 (2019). Reviewer: Georg Loho (Berlin) MSC: 14T20 52B20 14B05 PDFBibTeX XMLCite \textit{T. Takahashi}, Tokyo J. Math. 42, No. 1, 51--61 (2019; Zbl 1437.14068) Full Text: arXiv Euclid
Bùi, Nguyen Thao Nguyên; Phạm, Tien-Son Analytically principal part of polynomials at infinity. (English) Zbl 1365.14078 Ann. Pol. Math. 117, No. 3, 259-268 (2016). Reviewer: Aleksandr G. Aleksandrov (Moskva) MSC: 14P10 32S05 58K05 PDFBibTeX XMLCite \textit{N. T. N. Bùi} and \textit{T.-S. Phạm}, Ann. Pol. Math. 117, No. 3, 259--268 (2016; Zbl 1365.14078) Full Text: DOI
Abderrahmane, Ould M. On deformation with constant Milnor number and Newton polyhedron. (English) Zbl 1369.14007 Math. Z. 284, No. 1-2, 167-174 (2016). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 14B05 32S05 PDFBibTeX XMLCite \textit{O. M. Abderrahmane}, Math. Z. 284, No. 1--2, 167--174 (2016; Zbl 1369.14007) Full Text: DOI arXiv
Esterov, Alexander; Gusev, Gleb Multivariate Abel-Ruffini. (English) Zbl 1371.14059 Math. Ann. 365, No. 3-4, 1091-1110 (2016). Reviewer: Serge Lawrencenko (Moskva) MSC: 14M25 12F10 20B15 52B20 PDFBibTeX XMLCite \textit{A. Esterov} and \textit{G. Gusev}, Math. Ann. 365, No. 3--4, 1091--1110 (2016; Zbl 1371.14059) Full Text: DOI arXiv
Khovanskii, A. G. Newton polytopes and irreducible components of complete intersections. (English. Russian original) Zbl 1370.14043 Izv. Math. 80, No. 1, 263-284 (2016); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 80, No. 1, 281-304 (2016). Reviewer: Serge Lawrencenko (Moskva) MSC: 14M25 32B20 13P15 52A39 52B20 32Q55 PDFBibTeX XMLCite \textit{A. G. Khovanskii}, Izv. Math. 80, No. 1, 263--284 (2016; Zbl 1370.14043); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 80, No. 1, 281--304 (2016) Full Text: DOI
Búi, Nguyễn Thao Nguyên; Phạm, Tiến So’n Computation of the łojasiewicz exponent of nonnegative and nondegenerate analytic functions. (English) Zbl 1310.32010 Int. J. Math. 25, No. 10, Article ID 1450092, 13 p. (2014). Reviewer: Armin Rainer (Wien) MSC: 32B20 32S05 PDFBibTeX XMLCite \textit{N. T. N. Búi} and \textit{T. S. Phạm}, Int. J. Math. 25, No. 10, Article ID 1450092, 13 p. (2014; Zbl 1310.32010) Full Text: DOI
Vui, Hà Huy Global Hölderian error bound for nondegenerate polynomials. (English) Zbl 1273.32014 SIAM J. Optim. 23, No. 2, 917-933 (2013). MSC: 32B20 14P10 PDFBibTeX XMLCite \textit{H. H. Vui}, SIAM J. Optim. 23, No. 2, 917--933 (2013; Zbl 1273.32014) Full Text: DOI
Kaveh, Kiumars; Khovanskii, A. G. Mixed volume and an extension of intersection theory of divisors. (English) Zbl 1287.14001 Mosc. Math. J. 10, No. 2, 343-375 (2010). Reviewer: Serge Lawrencenko (Moskva) MSC: 14C20 14C17 14M25 52A39 PDFBibTeX XMLCite \textit{K. Kaveh} and \textit{A. G. Khovanskii}, Mosc. Math. J. 10, No. 2, 343--375 (2010; Zbl 1287.14001) Full Text: arXiv Link
Walewska, Justyna The second jump of Milnor numbers. (English) Zbl 1202.32024 Demonstr. Math. 43, No. 2, 361-374 (2010). Reviewer: Karl Schwede (Ann Arbor) MSC: 32S30 14B07 14H20 PDFBibTeX XMLCite \textit{J. Walewska}, Demonstr. Math. 43, No. 2, 361--374 (2010; Zbl 1202.32024) Full Text: DOI
Bivià-Ausina, Carles Local Łojasiewicz exponents, Milnor numbers and mixed multiplicities of ideals. (English) Zbl 1168.32022 Math. Z. 262, No. 2, 389-409 (2009). Reviewer: Alexander Esterov (Moscow) MSC: 32S05 13H15 14B05 14M25 52B20 PDFBibTeX XMLCite \textit{C. Bivià-Ausina}, Math. Z. 262, No. 2, 389--409 (2009; Zbl 1168.32022) Full Text: DOI Link
Philippon, Patrice; Sombra, Martín A refinement of the Bernštein-Kušnirenko estimate. (English) Zbl 1155.14037 Adv. Math. 218, No. 5, 1370-1418 (2008). Reviewer: Boris Kunyavskii (Ramat Gan) MSC: 14M25 14C17 11G50 14G40 52A99 32A05 PDFBibTeX XMLCite \textit{P. Philippon} and \textit{M. Sombra}, Adv. Math. 218, No. 5, 1370--1418 (2008; Zbl 1155.14037) Full Text: DOI arXiv
Philippon, Patrice; Sombra, Martín Une nouvelle majoration pour le nombre de solutions d’un système d’équations polynomiales. (A new estimate for the number of solutions of a system of polynomial equations.) (French) Zbl 1128.14039 C. R., Math., Acad. Sci. Paris 345, No. 6, 335-340 (2007). Reviewer: Boris Kunyavskii (Ramat Gan) MSC: 14M25 14G05 PDFBibTeX XMLCite \textit{P. Philippon} and \textit{M. Sombra}, C. R., Math., Acad. Sci. Paris 345, No. 6, 335--340 (2007; Zbl 1128.14039) Full Text: DOI
Braun, Gábor; Némethi, András Invariants of Newton non-degenerate surface singularities. (English) Zbl 1124.14033 Compos. Math. 143, No. 4, 1003-1036 (2007). Reviewer: Tadashi Tomaru (Maebashi) MSC: 14J17 14Q10 PDFBibTeX XMLCite \textit{G. Braun} and \textit{A. Némethi}, Compos. Math. 143, No. 4, 1003--1036 (2007; Zbl 1124.14033) Full Text: DOI arXiv
Barroso, Evelia García; Krasiński, Tadeusz; Płoski, Arkadiusz The Łojasiewicz numbers and plane curve singularities. (English) Zbl 1095.32010 Ann. Pol. Math. 87, 127-150 (2005). Reviewer: Carles Biviá-Ausina (València) MSC: 32S05 14H20 PDFBibTeX XMLCite \textit{E. G. Barroso} et al., Ann. Pol. Math. 87, 127--150 (2005; Zbl 1095.32010) Full Text: DOI
Douai, Antoine; Sabbah, Claude Gauss-Manin systems, Brieskorn lattices and Frobenius structures. II. (English) Zbl 1079.32017 Hertling, Claus (ed.) et al., Frobenius manifolds. Quantum cohomology and singularities. Proceedings of the workshop, Bonn, Germany, July 8–19, 2002. Wiesbaden: Vieweg (ISBN 3-528-03206-5/hbk ). Aspects of Mathematics E 36, 1-18 (2004). Reviewer: Hossein Movasati (Tokyo) MSC: 32S40 PDFBibTeX XMLCite \textit{A. Douai} and \textit{C. Sabbah}, in: Frobenius manifolds. Quantum cohomology and singularities. Proceedings of the workshop, Bonn, Germany, July 8--19, 2002. Wiesbaden: Vieweg. 1--18 (2004; Zbl 1079.32017) Full Text: arXiv
Furuya, Masako Lower bound of Newton number. (English) Zbl 1072.14003 Tokyo J. Math. 27, No. 1, 177-186 (2004). Reviewer: Carlos Galindo (Castellon) MSC: 14B05 32S05 PDFBibTeX XMLCite \textit{M. Furuya}, Tokyo J. Math. 27, No. 1, 177--186 (2004; Zbl 1072.14003) Full Text: DOI arXiv
Douai, Antoine; Sabbah, Claude Gauss-Manin systems, Brieskorn lattices and Frobenius structures. I. (English) Zbl 1079.32016 Ann. Inst. Fourier 53, No. 4, 1055-1116 (2003). Reviewer: Hossein Movasati (Tokyo) MSC: 32S40 PDFBibTeX XMLCite \textit{A. Douai} and \textit{C. Sabbah}, Ann. Inst. Fourier 53, No. 4, 1055--1116 (2003; Zbl 1079.32016) Full Text: DOI arXiv Numdam EuDML
Bivià-Ausina, Carles; Fukui, Toshizumi; Saia, Marcelo José Newton filtrations, graded algebras and codimension of non-degenerate ideals. (English) Zbl 1059.14004 Math. Proc. Camb. Philos. Soc. 133, No. 1, 55-75 (2002). MSC: 14B05 14Q10 14M25 32S05 PDFBibTeX XMLCite \textit{C. Bivià-Ausina} et al., Math. Proc. Camb. Philos. Soc. 133, No. 1, 55--75 (2002; Zbl 1059.14004) Full Text: DOI
Ishikawa, Masaharu The bifurcation set of a complex polynomial function of two variables and the Newton polygons of singularities at infinity. (English) Zbl 1023.32016 J. Math. Soc. Japan 54, No. 1, 161-196 (2002). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 32S05 32S15 32S50 32S55 PDFBibTeX XMLCite \textit{M. Ishikawa}, J. Math. Soc. Japan 54, No. 1, 161--196 (2002; Zbl 1023.32016) Full Text: DOI
Lenarcik, Andrzej; Płoski, Arkasiusz Polar invariants of plane curves and the Newton polygon. (English) Zbl 0984.32018 Kodai Math. J. 23, No. 3, 309-319 (2000). Reviewer: C.Bivià-Ausina (Valencia) MSC: 32S55 PDFBibTeX XMLCite \textit{A. Lenarcik} and \textit{A. Płoski}, Kodai Math. J. 23, No. 3, 309--319 (2000; Zbl 0984.32018) Full Text: DOI Link
Maillot, Vincent An arithmetic Bernstein-Koushnirenko theorem. (Un théorème de Bernstein-Koushnirenko arithmétique.) (French) Zbl 0870.14015 C. R. Acad. Sci., Paris, Sér. I 323, No. 9, 977-980 (1996). Reviewer: Doru Ştefănescu (Bucureşti) MSC: 14G05 14M25 11G99 14G25 PDFBibTeX XMLCite \textit{V. Maillot}, C. R. Acad. Sci., Paris, Sér. I 323, No. 9, 977--980 (1996; Zbl 0870.14015)
Brion, Michel Piecewise polynomial functions, convex polytopes and enumerative geometry. (English) Zbl 0878.14035 Pragacz, Piotr (ed.), Parameter spaces: enumerative geometry, algebra and combinatorics. Proceedings of the Banach Center conference, Warsaw, Poland, February 1994. Warszawa: Inst. of Math., Polish Acad. of Sciences, Banach Cent. Publ. 36, 25-44 (1996). Reviewer: D.Laksov (Stockholm) MSC: 14M25 14N10 14M17 52A20 PDFBibTeX XMLCite \textit{M. Brion}, Banach Cent. Publ. 36, 25--44 (1996; Zbl 0878.14035) Full Text: EuDML
Adolphson, Alan; Sperber, Steven Exponential sums and Newton polyhedra. (English) Zbl 0634.12018 Bull. Am. Math. Soc., New Ser. 16, 282-286 (1987). Reviewer: F.Baldassarri MSC: 11T23 14F20 11L03 PDFBibTeX XMLCite \textit{A. Adolphson} and \textit{S. Sperber}, Bull. Am. Math. Soc., New Ser. 16, 282--286 (1987; Zbl 0634.12018) Full Text: DOI
Martin, Bernd; Pfister, Gerhard Milnor number of complete intersections and Newton polygons. (English) Zbl 0556.32004 Math. Nachr. 110, 159-177 (1983). Reviewer: A.Dimca MSC: 32S05 58C15 14M10 14B05 PDFBibTeX XMLCite \textit{B. Martin} and \textit{G. Pfister}, Math. Nachr. 110, 159--177 (1983; Zbl 0556.32004) Full Text: DOI
Pfister, Gerhard Invariants of singularities and Newton polyhedron. (English) Zbl 0481.14001 Algebraic geometry, Proc., Bucharest 1980, 123-138 (1981). MSC: 14B05 58C15 14J17 58C25 58K99 14B07 PDFBibTeX XML
Israilov, M. I. Numbers of solutions of linear Diophantine equations and their applications in the theory of invariant cubature formulas. (English) Zbl 0467.10010 Sib. Math. J. 22, 260-273 (1981). MSC: 11D04 65D32 52Bxx PDFBibTeX XMLCite \textit{M. I. Israilov}, Sib. Math. J. 22, 260--273 (1981; Zbl 0467.10010) Full Text: DOI
Israilov, M. I. Determination of the number of solutions of linear Diophantine equations and its applications in the theory of invariant cubature formulas. (Russian) Zbl 0459.10010 Sib. Mat. Zh. 22, No. 2, 121-136 (1981). MSC: 11D04 PDFBibTeX XMLCite \textit{M. I. Israilov}, Sib. Mat. Zh. 22, No. 2, 121--136 (1981; Zbl 0459.10010) Full Text: EuDML
Merle, M.; Teissier, B. Conditions d’adjonction. (D’apres Du Val). (French) Zbl 0461.14009 Semin. sur les singularites des surfaces, Cent. Math. Ec. Polytech., Palaiseau 1976-77, Lect. Notes Math. 777, 229-245 (1980). MSC: 14J17 14B05 32S05 32B10 PDFBibTeX XML Full Text: Numdam EuDML
Merle, M. Les anneaux coniques sont de Cohen-Macaulay. (D’apres A.G. Kouchnirenko). (French) Zbl 0449.13009 Semin. sur les singularites des surfaces, Cent. Math. Ec. Polytech., Palaiseau 1976-77, Lect. Notes Math. 777, 295-302 (1980). MSC: 13H10 14M05 14H20 PDFBibTeX XML Full Text: Numdam EuDML
Pkhedotov, V. P. A new method of proving inequalities between mixed volumes and a generalization of the Aleksandrov-Fenchel-Shephard inequalities. (English. Russian original) Zbl 0432.52007 Sov. Math., Dokl. 20, 268-271 (1979); translation from Dokl. Akad. Nauk SSSR 245, 31-34 (1979). MSC: 52A20 52A40 PDFBibTeX XMLCite \textit{V. P. Pkhedotov}, Sov. Math., Dokl. 20, 268--271 (1979; Zbl 0432.52007); translation from Dokl. Akad. Nauk SSSR 245, 31--34 (1979)
Kirillov, A. N. Commutative formal groups. (Russian) Zbl 0359.14014 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 57, 117-124 (1976). Reviewer: Yu. G. Zarhin MSC: 14L05 14D10 PDFBibTeX XMLCite \textit{A. N. Kirillov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 57, 117--124 (1976; Zbl 0359.14014)