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Author ID: batyrev.victor-v Recent zbMATH articles by "Batyrev, Victor V."
Published as: Batyrev, Victor V.; Batyrev, Victor; Batyrev, V. V.; Batyrev, V.
Homepage: https://www.math.uni-tuebingen.de/de/forschung/algebra/personen/prof-dr-victor-b...
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Publications by Year

Citations contained in zbMATH Open

49 Publications have been cited 1,681 times in 1,037 Documents Cited by Year
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. Zbl 0829.14023
Batyrev, Victor V.
358
1994
On the Hodge structure of projective hypersurfaces in toric varieties. Zbl 0851.14021
Batyrev, Victor V.; Cox, David A.
76
1994
On Calabi-Yau complete intersections in toric varieties. Zbl 0908.14015
Batyrev, Victor V.; Borisov, Lev A.
70
1996
On the number of rational points of bounded height on algebraic varieties. (Sur le nombre des points rationnels de hauteur borné des variétés algébriques.) Zbl 0679.14008
Batyrev, V. V.; Manin, Yu. I.
70
1990
Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori. Zbl 0812.14035
Batyrev, Victor V.
69
1993
On the classification of toric Fano 4-folds. Zbl 0929.14024
Batyrev, V. V.
66
1999
Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry. Zbl 0864.14022
Batyrev, Victor V.; Dais, Dimitrios I.
58
1996
Mirror symmetry and toric degenerations of partial flag manifolds. Zbl 1022.14014
Batyrev, Victor V.; Ciocan-Fontanine, Ionuţ; Kim, Bumsig; van Straten, Duco
56
2000
Stringy Hodge numbers of varieties with Gorenstein canonical singularities. Zbl 0963.14015
Batyrev, Victor V.
55
1998
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties. Zbl 0843.14016
Batyrev, Victor V.; van Straten, Duco
54
1995
On the classification of smooth projective toric varieties. Zbl 0792.14026
Batyrev, Victor V.
53
1991
Mirror duality and string-theoretic Hodge numbers. Zbl 0872.14035
Batyrev, Victor V.; Borisov, Lev A.
53
1996
Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians. Zbl 0896.14025
Batyrev, V. V.; Ciocan-Fontanine, I.; Kim, B.; Van Straten, D.
50
1998
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. Zbl 0943.14004
Batyrev, Victor V.
48
1999
Quantum cohomology rings of toric manifolds. Zbl 0806.14041
Batyrev, Victor V.
47
1993
Manin’s conjecture for toric varieties. Zbl 0946.14009
Batyrev, Victor V.; Tschinkel, Yuri
35
1998
The Cox ring of a del Pezzo surface. Zbl 1075.14035
Batyrev, Victor V.; Popov, Oleg N.
34
2004
Dual cones and mirror symmetry for generalized Calabi-Yau manifolds. Zbl 0927.14019
Batyrev, Victor V.; Borisov, Lev A.
33
1997
Tamagawa numbers of polarized algebraic varieties. Zbl 0926.11045
Batyrev, Victor V.; Tschinkel, Yuri
32
1998
Combinatorial aspects of mirror symmetry. Zbl 1161.14037
Batyrev, Victor; Nill, Benjamin
32
2008
Birational Calabi-Yau \(n\)-folds have equal Betti numbers. Zbl 0955.14028
Batyrev, Victor V.
29
1999
Rational points of bounded height on compactifications of anisotropic tori. Zbl 0890.14008
Batyrev, Victor V.; Tschinkel, Yuri
26
1995
Toric Fano threefolds. Zbl 0478.14032
Batyrev, V. V.
24
1981
Integral cohomology and mirror symmetry for Calabi-Yau 3-folds. Zbl 1116.14033
Batyrev, Victor; Kreuzer, Maximilian
23
2006
Toroidal Fano 3-folds. Zbl 0495.14027
Batyrev, V. V.
23
1982
Einstein-Kähler metrics on symmetric toric Fano manifolds. Zbl 0939.32016
Batyrev, Victor V.; Selivanova, Elena N.
21
1999
Rational points on some Fano cubic bundles. Zbl 0879.14007
Batyrev, Victor V.; Tschinkel, Yuri
21
1996
Multiples of lattice polytopes without interior lattice points. Zbl 1134.52020
Batyrev, Victor; Nill, Benjamin
21
2007
Height zeta functions of toric varieties. Zbl 0915.14013
Batyrev, V.; Tschinkel, Yu.
18
1996
Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions. Zbl 1242.14037
Batyrev, Victor; Kreuzer, Maximilian
17
2010
The cone of effective divisors of threefolds. Zbl 0781.14027
Batyrev, Victor V.
14
1992
Toric degenerations of Fano varieties and constructing mirror manifolds. Zbl 1072.14070
Batyrev, Victor V.
12
2004
The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces. Zbl 1255.14041
Batyrev, Victor; Blume, Mark
11
2011
The arc space of horospherical varieties and motivic integration. Zbl 1291.14027
Batyrev, Victor; Moreau, Anne
10
2013
Toric residues and mirror symmetry. Zbl 1026.14016
Batyrev, Victor V.; Materov, Evgeny N.
9
2002
Classification of Gorenstein toric del Pezzo varieties in arbitrary dimension. Zbl 1235.14043
Batyrev, Victor; Juny, Dorothee
7
2010
Stringy Chern classes of singular toric varieties and their applications. Zbl 1444.14075
Batyrev, Victor; Schaller, Karin
7
2017
The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality. Zbl 1400.14139
Batyrev, Victor
6
2017
Mixed tori residues and Calabi-Yau complete intersections. Zbl 1060.14074
Batyrev, Victor V.; Materov, Evgeny N.
6
2003
On generalisations of Losev-Manin moduli spaces for classical root systems. Zbl 1316.14050
Batyrev, Victor; Blume, Mark
5
2011
Lattice polytopes with a given \(h^*\)-polynomial. Zbl 1121.52026
Batyrev, Victor V.
5
2006
On the geometry of \(SL(2)\)-equivariant flips. Zbl 1221.14052
Batyrev, Victor; Haddad, Fatima
5
2008
Boundedness of the degree of multidimensional toric Fano varieties. Zbl 0505.14033
Batyrev, V. V.
4
1982
Stringy Hodge numbers and Virasoro algebra. Zbl 0952.14038
Batyrev, Victor V.
3
2000
Satellites of spherical subgroups. Zbl 1472.14048
Batyrev, Victor; Moreau, Anne
1
2020
Rational points on toric varieties. Zbl 0871.14040
Batyrev, V. V.; Tschinkel, Yu.
1
1995
Mirror symmetry and toric geometry. Zbl 0933.14020
Batyrev, Victor V.
1
1998
Stringy \(E\)-functions of canonical toric Fano threefolds and their applications. Zbl 1427.14107
Batyrev, V. V.; Schaller, K.
1
2019
A theorem on non-extensibility of toric varieties. Zbl 0618.14029
Batyrev, V. V.; Mel’nikov, D. A.
1
1986
Satellites of spherical subgroups. Zbl 1472.14048
Batyrev, Victor; Moreau, Anne
1
2020
Stringy \(E\)-functions of canonical toric Fano threefolds and their applications. Zbl 1427.14107
Batyrev, V. V.; Schaller, K.
1
2019
Stringy Chern classes of singular toric varieties and their applications. Zbl 1444.14075
Batyrev, Victor; Schaller, Karin
7
2017
The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality. Zbl 1400.14139
Batyrev, Victor
6
2017
The arc space of horospherical varieties and motivic integration. Zbl 1291.14027
Batyrev, Victor; Moreau, Anne
10
2013
The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces. Zbl 1255.14041
Batyrev, Victor; Blume, Mark
11
2011
On generalisations of Losev-Manin moduli spaces for classical root systems. Zbl 1316.14050
Batyrev, Victor; Blume, Mark
5
2011
Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions. Zbl 1242.14037
Batyrev, Victor; Kreuzer, Maximilian
17
2010
Classification of Gorenstein toric del Pezzo varieties in arbitrary dimension. Zbl 1235.14043
Batyrev, Victor; Juny, Dorothee
7
2010
Combinatorial aspects of mirror symmetry. Zbl 1161.14037
Batyrev, Victor; Nill, Benjamin
32
2008
On the geometry of \(SL(2)\)-equivariant flips. Zbl 1221.14052
Batyrev, Victor; Haddad, Fatima
5
2008
Multiples of lattice polytopes without interior lattice points. Zbl 1134.52020
Batyrev, Victor; Nill, Benjamin
21
2007
Integral cohomology and mirror symmetry for Calabi-Yau 3-folds. Zbl 1116.14033
Batyrev, Victor; Kreuzer, Maximilian
23
2006
Lattice polytopes with a given \(h^*\)-polynomial. Zbl 1121.52026
Batyrev, Victor V.
5
2006
The Cox ring of a del Pezzo surface. Zbl 1075.14035
Batyrev, Victor V.; Popov, Oleg N.
34
2004
Toric degenerations of Fano varieties and constructing mirror manifolds. Zbl 1072.14070
Batyrev, Victor V.
12
2004
Mixed tori residues and Calabi-Yau complete intersections. Zbl 1060.14074
Batyrev, Victor V.; Materov, Evgeny N.
6
2003
Toric residues and mirror symmetry. Zbl 1026.14016
Batyrev, Victor V.; Materov, Evgeny N.
9
2002
Mirror symmetry and toric degenerations of partial flag manifolds. Zbl 1022.14014
Batyrev, Victor V.; Ciocan-Fontanine, Ionuţ; Kim, Bumsig; van Straten, Duco
56
2000
Stringy Hodge numbers and Virasoro algebra. Zbl 0952.14038
Batyrev, Victor V.
3
2000
On the classification of toric Fano 4-folds. Zbl 0929.14024
Batyrev, V. V.
66
1999
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. Zbl 0943.14004
Batyrev, Victor V.
48
1999
Birational Calabi-Yau \(n\)-folds have equal Betti numbers. Zbl 0955.14028
Batyrev, Victor V.
29
1999
Einstein-Kähler metrics on symmetric toric Fano manifolds. Zbl 0939.32016
Batyrev, Victor V.; Selivanova, Elena N.
21
1999
Stringy Hodge numbers of varieties with Gorenstein canonical singularities. Zbl 0963.14015
Batyrev, Victor V.
55
1998
Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians. Zbl 0896.14025
Batyrev, V. V.; Ciocan-Fontanine, I.; Kim, B.; Van Straten, D.
50
1998
Manin’s conjecture for toric varieties. Zbl 0946.14009
Batyrev, Victor V.; Tschinkel, Yuri
35
1998
Tamagawa numbers of polarized algebraic varieties. Zbl 0926.11045
Batyrev, Victor V.; Tschinkel, Yuri
32
1998
Mirror symmetry and toric geometry. Zbl 0933.14020
Batyrev, Victor V.
1
1998
Dual cones and mirror symmetry for generalized Calabi-Yau manifolds. Zbl 0927.14019
Batyrev, Victor V.; Borisov, Lev A.
33
1997
On Calabi-Yau complete intersections in toric varieties. Zbl 0908.14015
Batyrev, Victor V.; Borisov, Lev A.
70
1996
Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry. Zbl 0864.14022
Batyrev, Victor V.; Dais, Dimitrios I.
58
1996
Mirror duality and string-theoretic Hodge numbers. Zbl 0872.14035
Batyrev, Victor V.; Borisov, Lev A.
53
1996
Rational points on some Fano cubic bundles. Zbl 0879.14007
Batyrev, Victor V.; Tschinkel, Yuri
21
1996
Height zeta functions of toric varieties. Zbl 0915.14013
Batyrev, V.; Tschinkel, Yu.
18
1996
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties. Zbl 0843.14016
Batyrev, Victor V.; van Straten, Duco
54
1995
Rational points of bounded height on compactifications of anisotropic tori. Zbl 0890.14008
Batyrev, Victor V.; Tschinkel, Yuri
26
1995
Rational points on toric varieties. Zbl 0871.14040
Batyrev, V. V.; Tschinkel, Yu.
1
1995
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. Zbl 0829.14023
Batyrev, Victor V.
358
1994
On the Hodge structure of projective hypersurfaces in toric varieties. Zbl 0851.14021
Batyrev, Victor V.; Cox, David A.
76
1994
Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori. Zbl 0812.14035
Batyrev, Victor V.
69
1993
Quantum cohomology rings of toric manifolds. Zbl 0806.14041
Batyrev, Victor V.
47
1993
The cone of effective divisors of threefolds. Zbl 0781.14027
Batyrev, Victor V.
14
1992
On the classification of smooth projective toric varieties. Zbl 0792.14026
Batyrev, Victor V.
53
1991
On the number of rational points of bounded height on algebraic varieties. (Sur le nombre des points rationnels de hauteur borné des variétés algébriques.) Zbl 0679.14008
Batyrev, V. V.; Manin, Yu. I.
70
1990
A theorem on non-extensibility of toric varieties. Zbl 0618.14029
Batyrev, V. V.; Mel’nikov, D. A.
1
1986
Toroidal Fano 3-folds. Zbl 0495.14027
Batyrev, V. V.
23
1982
Boundedness of the degree of multidimensional toric Fano varieties. Zbl 0505.14033
Batyrev, V. V.
4
1982
Toric Fano threefolds. Zbl 0478.14032
Batyrev, V. V.
24
1981
all top 5

Cited by 1,081 Authors

20 Nill, Benjamin
19 Klemm, Albrecht
18 Morrison, David R.
15 Higashitani, Akihiro
15 Tsuchiya, Akiyoshi
13 Batyrev, Victor V.
13 Borisov, Lev A.
13 Braun, Andreas P.
12 Yau, Shing-Tung
11 Derenthal, Ulrich
11 Hibi, Takayuki
11 Hosono, Shinobu
10 Browning, Timothy Daniel
10 de la Bretèche, Régis
10 Katz, Sheldon
10 Stapledon, Alan
10 Taylor, Washington IV
9 Candelas, Philip
9 Greene, Brian R.
9 Kreuzer, Maximilian
9 Lian, Bong H.
9 Ohsugi, Hidefumi
9 Tanimoto, Sho
8 Aspinwall, Paul S.
8 Casagrande, Cinzia
8 Jockers, Hans
8 Michałek, Mateusz
8 Rossi, Michele
8 Sato, Hiroshi
8 Skarke, Harald
8 Tschinkel, Yuri
8 Ueda, Kazushi
7 Cho, Yunhyung
7 Grassi, Antonella
7 Gross, Mark
7 He, Yang-Hui Evariste
7 Kasprzyk, Alexander M.
7 Lehmann, Brian
7 Loughran, Daniel
7 Mase, Makiko
7 van Straten, Duco
7 Yasuda, Takehiko
6 Blumenhagen, Ralph
6 Coates, Tom
6 Dais, Dimitrios I.
6 Dickenstein, Alicia M.
6 Doran, Charles F.
6 Gagliardi, Giuliano
6 Grassi, Alba
6 Gray, James A.
6 Haase, Christian Alexander
6 Hausen, Jürgen
6 Laface, Antonio
6 Mayr, Peter
6 Oehlmann, Paul-Konstantin
6 Ruan, Yongbin
6 Schimannek, Thorsten
6 Sturmfels, Bernd
6 Terracini, Lea
5 Berglund, Per
5 Bruzzo, Ugo
5 Font, Anamaría
5 Grimm, Thomas W.
5 Iritani, Hiroshi
5 Kim, Bumsig
5 Kim, Yoosik
5 Klevers, Denis
5 Mavlyutov, Anvar R.
5 Peyre, Emmanuel
5 Przhiyalkovskiĭ, Viktor Vladimirovich
5 Quevedo Rodriguez, Fernando
5 Rietsch, Konstanze
5 Sano, Yuji
5 Schepers, Jan
5 Sperber, Steven I.
5 Takloo-Bighash, Ramin
5 Valandro, Roberto
5 Velasco, Mauricio
4 Adolphson, Alan
4 Altmann, Klaus
4 Artebani, Michela
4 Balletti, Gabriele
4 Beck, Matthias
4 Belavin, Aleksandr Abramovich
4 Berman, Robert J.
4 Bourqui, David
4 Braun, Benjamin
4 Braun, Volker
4 Castryck, Wouter
4 Cattani, Eduardo H.
4 Chan, Kwokwai
4 Ciocan-Fontanine, Ionuţ
4 de Fernex, Tommaso
4 de la Ossa, Xenia C.
4 Frías Medina, Juan Bosco
4 Gu, Jie
4 Hanany, Amihay
4 Horja, Richard Paul
4 Huang, Minxin
4 Katz, Eric
...and 981 more Authors
all top 5

Cited in 184 Serials

84 Journal of High Energy Physics
59 Advances in Mathematics
53 Nuclear Physics. B
39 Communications in Mathematical Physics
34 Duke Mathematical Journal
26 Mathematische Zeitschrift
25 Tôhoku Mathematical Journal. Second Series
22 Journal of Geometry and Physics
21 Transactions of the American Mathematical Society
21 Journal of Algebraic Geometry
18 Proceedings of the American Mathematical Society
17 Journal of Algebra
17 Manuscripta Mathematica
16 Compositio Mathematica
15 Mathematische Annalen
14 Annales de l’Institut Fourier
14 European Journal of Mathematics
13 International Journal of Mathematics
12 Journal of Pure and Applied Algebra
12 Journal of the American Mathematical Society
11 Journal of Number Theory
11 Journal für die Reine und Angewandte Mathematik
10 Geometriae Dedicata
10 Inventiones Mathematicae
10 Journal of Combinatorial Theory. Series A
10 Discrete & Computational Geometry
10 Geometry & Topology
9 Michigan Mathematical Journal
9 The Electronic Journal of Combinatorics
9 Transformation Groups
8 Communications in Algebra
8 Proceedings of the Steklov Institute of Mathematics
7 Nagoya Mathematical Journal
7 European Journal of Combinatorics
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
7 Journal of Algebraic Combinatorics
7 Journal de Théorie des Nombres de Bordeaux
7 Selecta Mathematica. New Series
7 Advances in High Energy Physics
6 Israel Journal of Mathematics
6 Nuclear Physics. B. Proceedings Supplements
6 Journal of Mathematical Sciences (New York)
6 Advances in Geometry
6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
5 Journal of Mathematical Physics
5 Mathematical Proceedings of the Cambridge Philosophical Society
5 Beiträge zur Algebra und Geometrie
5 Proceedings of the Japan Academy. Series A
5 Journal of the European Mathematical Society (JEMS)
5 Algebra & Number Theory
5 Kyoto Journal of Mathematics
5 Forum of Mathematics, Sigma
4 International Journal of Modern Physics A
4 Letters in Mathematical Physics
4 Theoretical and Mathematical Physics
4 Mathematics of Computation
4 Fortschritte der Physik
4 Collectanea Mathematica
4 Mathematische Nachrichten
4 Annals of Combinatorics
4 Communications in Contemporary Mathematics
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Research in the Mathematical Sciences
3 Modern Physics Letters A
3 Physics Letters. B
3 Arkiv för Matematik
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Bulletin de la Société Mathématique de France
3 Canadian Journal of Mathematics
3 Le Matematiche
3 Mathematika
3 Memoirs of the American Mathematical Society
3 Bulletin of the Korean Mathematical Society
3 Annals of Global Analysis and Geometry
3 Forum Mathematicum
3 Linear Algebra and its Applications
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Izvestiya: Mathematics
3 Documenta Mathematica
3 Annals of Mathematics. Second Series
3 Annales Henri Poincaré
3 Bulletin of the Brazilian Mathematical Society. New Series
3 Central European Journal of Mathematics
3 Journal of Physics A: Mathematical and Theoretical
3 Science China. Mathematics
2 Bulletin of the Australian Mathematical Society
2 Discrete Mathematics
2 Rocky Mountain Journal of Mathematics
2 Reviews in Mathematical Physics
2 Acta Mathematica
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Illinois Journal of Mathematics
2 Journal of the Korean Mathematical Society
2 Monatshefte für Mathematik
2 Proceedings of the Edinburgh Mathematical Society. Series II
2 Publications of the Research Institute for Mathematical Sciences, Kyoto University
2 Results in Mathematics
2 Tokyo Journal of Mathematics
2 Advances in Applied Mathematics
2 Journal of Symbolic Computation
...and 84 more Serials
all top 5

Cited in 45 Fields

853 Algebraic geometry (14-XX)
205 Quantum theory (81-XX)
167 Several complex variables and analytic spaces (32-XX)
141 Convex and discrete geometry (52-XX)
138 Number theory (11-XX)
118 Differential geometry (53-XX)
62 Commutative algebra (13-XX)
61 Relativity and gravitational theory (83-XX)
37 Combinatorics (05-XX)
34 Special functions (33-XX)
32 Manifolds and cell complexes (57-XX)
27 Global analysis, analysis on manifolds (58-XX)
19 Algebraic topology (55-XX)
15 Nonassociative rings and algebras (17-XX)
15 Group theory and generalizations (20-XX)
13 Dynamical systems and ergodic theory (37-XX)
10 Associative rings and algebras (16-XX)
9 Order, lattices, ordered algebraic structures (06-XX)
9 Category theory; homological algebra (18-XX)
7 \(K\)-theory (19-XX)
7 Topological groups, Lie groups (22-XX)
7 Computer science (68-XX)
6 Partial differential equations (35-XX)
6 Geometry (51-XX)
5 Field theory and polynomials (12-XX)
5 Ordinary differential equations (34-XX)
4 Real functions (26-XX)
3 Mathematical logic and foundations (03-XX)
3 Functions of a complex variable (30-XX)
3 Approximations and expansions (41-XX)
3 Mechanics of particles and systems (70-XX)
3 Information and communication theory, circuits (94-XX)
2 Difference and functional equations (39-XX)
2 Abstract harmonic analysis (43-XX)
2 Operator theory (47-XX)
2 Statistical mechanics, structure of matter (82-XX)
2 Operations research, mathematical programming (90-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Measure and integration (28-XX)
1 Sequences, series, summability (40-XX)
1 General topology (54-XX)
1 Numerical analysis (65-XX)
1 Astronomy and astrophysics (85-XX)

Citations by Year

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