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Batyrev, Victor V.

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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...
External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · GND
Documents Indexed: 56 Publications since 1981, including 1 Book

Publications by Year

Citations contained in zbMATH Open

48 Publications have been cited 1,473 times in 916 Documents Cited by Year
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. Zbl 0829.14023
Batyrev, Victor V.
316
1994
On the Hodge structure of projective hypersurfaces in toric varieties. Zbl 0851.14021
Batyrev, Victor V.; Cox, David A.
66
1994
Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori. Zbl 0812.14035
Batyrev, Victor V.
63
1993
On Calabi-Yau complete intersections in toric varieties. Zbl 0908.14015
Batyrev, Victor V.; Borisov, Lev A.
62
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.
58
1990
Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry. Zbl 0864.14022
Batyrev, Victor V.; Dais, Dimitrios I.
55
1996
On the classification of toric Fano 4-folds. Zbl 0929.14024
Batyrev, V. V.
52
1999
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties. Zbl 0843.14016
Batyrev, Victor V.; van Straten, Duco
50
1995
Mirror duality and string-theoretic Hodge numbers. Zbl 0872.14035
Batyrev, Victor V.; Borisov, Lev A.
50
1996
On the classification of smooth projective toric varieties. Zbl 0792.14026
Batyrev, Victor V.
48
1991
Stringy Hodge numbers of varieties with Gorenstein canonical singularities. Zbl 0963.14015
Batyrev, Victor V.
48
1998
Quantum cohomology rings of toric manifolds. Zbl 0806.14041
Batyrev, Victor V.
44
1993
Mirror symmetry and toric degenerations of partial flag manifolds. Zbl 1022.14014
Batyrev, Victor V.; Ciocan-Fontanine, Ionuţ; Kim, Bumsig; van Straten, Duco
43
2000
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.
43
1998
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. Zbl 0943.14004
Batyrev, Victor V.
42
1999
Dual cones and mirror symmetry for generalized Calabi-Yau manifolds. Zbl 0927.14019
Batyrev, Victor V.; Borisov, Lev A.
32
1997
Manin’s conjecture for toric varieties. Zbl 0946.14009
Batyrev, Victor V.; Tschinkel, Yuri
32
1998
Combinatorial aspects of mirror symmetry. Zbl 1161.14037
Batyrev, Victor; Nill, Benjamin
31
2008
The Cox ring of a del Pezzo surface. Zbl 1075.14035
Batyrev, Victor V.; Popov, Oleg N.
31
2004
Tamagawa numbers of polarized algebraic varieties. Zbl 0926.11045
Batyrev, Victor V.; Tschinkel, Yuri
24
1998
Birational Calabi-Yau \(n\)-folds have equal Betti numbers. Zbl 0955.14028
Batyrev, Victor V.
23
1999
Rational points of bounded height on compactifications of anisotropic tori. Zbl 0890.14008
Batyrev, Victor V.; Tschinkel, Yuri
22
1995
Toroidal Fano 3-folds. Zbl 0495.14027
Batyrev, V. V.
22
1982
Toric Fano threefolds. Zbl 0478.14032
Batyrev, V. V.
21
1981
Integral cohomology and mirror symmetry for Calabi-Yau 3-folds. Zbl 1116.14033
Batyrev, Victor; Kreuzer, Maximilian
20
2006
Multiples of lattice polytopes without interior lattice points. Zbl 1134.52020
Batyrev, Victor; Nill, Benjamin
20
2007
Einstein-Kähler metrics on symmetric toric Fano manifolds. Zbl 0939.32016
Batyrev, Victor V.; Selivanova, Elena N.
19
1999
Rational points on some Fano cubic bundles. Zbl 0879.14007
Batyrev, Victor V.; Tschinkel, Yuri
18
1996
Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions. Zbl 1242.14037
Batyrev, Victor; Kreuzer, Maximilian
15
2010
Height zeta functions of toric varieties. Zbl 0915.14013
Batyrev, V.; Tschinkel, Yu.
13
1996
The cone of effective divisors of threefolds. Zbl 0781.14027
Batyrev, Victor V.
12
1992
Toric residues and mirror symmetry. Zbl 1026.14016
Batyrev, Victor V.; Materov, Evgeny N.
9
2002
The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces. Zbl 1255.14041
Batyrev, Victor; Blume, Mark
9
2011
Toric degenerations of Fano varieties and constructing mirror manifolds. Zbl 1072.14070
Batyrev, Victor V.
8
2004
The arc space of horospherical varieties and motivic integration. Zbl 1291.14027
Batyrev, Victor; Moreau, Anne
7
2013
Mixed tori residues and Calabi-Yau complete intersections. Zbl 1060.14074
Batyrev, Victor V.; Materov, Evgeny N.
6
2003
Classification of Gorenstein toric del Pezzo varieties in arbitrary dimension. Zbl 1235.14043
Batyrev, Victor; Juny, Dorothee
6
2010
Lattice polytopes with a given \(h^*\)-polynomial. Zbl 1121.52026
Batyrev, Victor V.
5
2006
Stringy Chern classes of singular toric varieties and their applications. Zbl 1444.14075
Batyrev, Victor; Schaller, Karin
5
2017
On generalisations of Losev-Manin moduli spaces for classical root systems. Zbl 1316.14050
Batyrev, Victor; Blume, Mark
5
2011
Boundedness of the degree of multidimensional toric Fano varieties. Zbl 0505.14033
Batyrev, V. V.
4
1982
On the geometry of \(SL(2)\)-equivariant flips. Zbl 1221.14052
Batyrev, Victor; Haddad, Fatima
4
2008
Stringy Hodge numbers and Virasoro algebra. Zbl 0952.14038
Batyrev, Victor V.
3
2000
The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality. Zbl 1400.14139
Batyrev, Victor
3
2017
Rational points on toric varieties. Zbl 0871.14040
Batyrev, V. V.; Tschinkel, Yu.
1
1995
A theorem on non-extensibility of toric varieties. Zbl 0618.14029
Batyrev, V. V.; Mel’nikov, D. A.
1
1986
Stringy \(E\)-functions of canonical toric Fano threefolds and their applications. Zbl 1427.14107
Batyrev, V. V.; Schaller, K.
1
2019
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
Stringy Chern classes of singular toric varieties and their applications. Zbl 1444.14075
Batyrev, Victor; Schaller, Karin
5
2017
The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality. Zbl 1400.14139
Batyrev, Victor
3
2017
The arc space of horospherical varieties and motivic integration. Zbl 1291.14027
Batyrev, Victor; Moreau, Anne
7
2013
The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces. Zbl 1255.14041
Batyrev, Victor; Blume, Mark
9
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
15
2010
Classification of Gorenstein toric del Pezzo varieties in arbitrary dimension. Zbl 1235.14043
Batyrev, Victor; Juny, Dorothee
6
2010
Combinatorial aspects of mirror symmetry. Zbl 1161.14037
Batyrev, Victor; Nill, Benjamin
31
2008
On the geometry of \(SL(2)\)-equivariant flips. Zbl 1221.14052
Batyrev, Victor; Haddad, Fatima
4
2008
Multiples of lattice polytopes without interior lattice points. Zbl 1134.52020
Batyrev, Victor; Nill, Benjamin
20
2007
Integral cohomology and mirror symmetry for Calabi-Yau 3-folds. Zbl 1116.14033
Batyrev, Victor; Kreuzer, Maximilian
20
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.
31
2004
Toric degenerations of Fano varieties and constructing mirror manifolds. Zbl 1072.14070
Batyrev, Victor V.
8
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
43
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.
52
1999
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. Zbl 0943.14004
Batyrev, Victor V.
42
1999
Birational Calabi-Yau \(n\)-folds have equal Betti numbers. Zbl 0955.14028
Batyrev, Victor V.
23
1999
Einstein-Kähler metrics on symmetric toric Fano manifolds. Zbl 0939.32016
Batyrev, Victor V.; Selivanova, Elena N.
19
1999
Stringy Hodge numbers of varieties with Gorenstein canonical singularities. Zbl 0963.14015
Batyrev, Victor V.
48
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.
43
1998
Manin’s conjecture for toric varieties. Zbl 0946.14009
Batyrev, Victor V.; Tschinkel, Yuri
32
1998
Tamagawa numbers of polarized algebraic varieties. Zbl 0926.11045
Batyrev, Victor V.; Tschinkel, Yuri
24
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.
32
1997
On Calabi-Yau complete intersections in toric varieties. Zbl 0908.14015
Batyrev, Victor V.; Borisov, Lev A.
62
1996
Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry. Zbl 0864.14022
Batyrev, Victor V.; Dais, Dimitrios I.
55
1996
Mirror duality and string-theoretic Hodge numbers. Zbl 0872.14035
Batyrev, Victor V.; Borisov, Lev A.
50
1996
Rational points on some Fano cubic bundles. Zbl 0879.14007
Batyrev, Victor V.; Tschinkel, Yuri
18
1996
Height zeta functions of toric varieties. Zbl 0915.14013
Batyrev, V.; Tschinkel, Yu.
13
1996
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties. Zbl 0843.14016
Batyrev, Victor V.; van Straten, Duco
50
1995
Rational points of bounded height on compactifications of anisotropic tori. Zbl 0890.14008
Batyrev, Victor V.; Tschinkel, Yuri
22
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.
316
1994
On the Hodge structure of projective hypersurfaces in toric varieties. Zbl 0851.14021
Batyrev, Victor V.; Cox, David A.
66
1994
Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori. Zbl 0812.14035
Batyrev, Victor V.
63
1993
Quantum cohomology rings of toric manifolds. Zbl 0806.14041
Batyrev, Victor V.
44
1993
The cone of effective divisors of threefolds. Zbl 0781.14027
Batyrev, Victor V.
12
1992
On the classification of smooth projective toric varieties. Zbl 0792.14026
Batyrev, Victor V.
48
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.
58
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.
22
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.
21
1981
all top 5

Cited by 970 Authors

20 Nill, Benjamin
18 Klemm, Albrecht
18 Morrison, David R.
13 Borisov, Lev A.
13 Tsuchiya, Akiyoshi
12 Batyrev, Victor V.
12 Braun, Andreas P.
11 Derenthal, Ulrich
11 Hibi, Takayuki
11 Higashitani, Akihiro
11 Yau, Shing-Tung
10 Browning, Timothy Daniel
10 de la Bretèche, Régis
10 Hosono, Shinobu
10 Katz, Sheldon
10 Stapledon, Alan
10 Taylor, Washington IV
9 Candelas, Philip
9 Greene, Brian R.
9 Kreuzer, Maximilian
8 Aspinwall, Paul S.
8 Jockers, Hans
8 Lian, Bong H.
8 Ohsugi, Hidefumi
8 Rossi, Michele
8 Skarke, Harald
8 Tschinkel, Yuri
8 Ueda, Kazushi
7 Grassi, Antonella
7 Loughran, Daniel
7 Michałek, Mateusz
7 Sato, Hiroshi
7 van Straten, Duco
6 Blumenhagen, Ralph
6 Casagrande, Cinzia
6 Dais, Dimitrios I.
6 Dickenstein, Alicia M.
6 Gagliardi, Giuliano
6 Grassi, Alba
6 Gross, Mark
6 Haase, Christian Alexander
6 He, Yang-Hui Evariste
6 Mase, Makiko
6 Mayr, Peter
6 Ruan, Yongbin
6 Sturmfels, Bernd
6 Terracini, Lea
5 Berglund, Per
5 Cho, Yunhyung
5 Doran, Charles F.
5 Font, Anamaría
5 Gray, James A.
5 Grimm, Thomas W.
5 Hausen, Jürgen
5 Iritani, Hiroshi
5 Kasprzyk, Alexander M.
5 Kim, Bumsig
5 Klevers, Denis
5 Laface, Antonio
5 Lehmann, Brian
5 Mavlyutov, Anvar R.
5 Oehlmann, Paul-Konstantin
5 Przhiyalkovskiĭ, Viktor Vladimirovich
5 Rietsch, Konstanze
5 Sano, Yuji
5 Schepers, Jan
5 Schimannek, Thorsten
5 Sperber, Steven I.
5 Tanimoto, Sho
5 Velasco, Mauricio
5 Yasuda, Takehiko
4 Adolphson, Alan
4 Altmann, Klaus
4 Artebani, Michela
4 Balletti, Gabriele
4 Bourqui, David
4 Braun, Volker
4 Castryck, Wouter
4 Cattani, Eduardo H.
4 Chan, Kwokwai
4 Ciocan-Fontanine, Ionuţ
4 Coates, Tom
4 de Fernex, Tommaso
4 de la Ossa, Xenia C.
4 Frías Medina, Juan Bosco
4 Horja, R. Paul
4 Huang, Minxin
4 Katz, Eric
4 Kim, Yoosik
4 Lahyane, Mustapha
4 Langlois, Kevin
4 Mariño, Marcos
4 Mayrhofer, Christoph
4 Paffenholz, Andreas
4 Peyre, Emmanuel
4 Quevedo Rodriguez, Fernando
4 Shramov, Konstantin Aleksandrovich
4 Takagi, Hiromichi
4 Takloo-Bighash, Ramin
4 Theisen, Stefan J.
...and 870 more Authors
all top 5

Cited in 167 Serials

69 Journal of High Energy Physics
55 Advances in Mathematics
53 Nuclear Physics. B
39 Communications in Mathematical Physics
33 Duke Mathematical Journal
25 Tohoku Mathematical Journal. Second Series
22 Journal of Geometry and Physics
21 Transactions of the American Mathematical Society
20 Journal of Algebraic Geometry
19 Mathematische Zeitschrift
18 Proceedings of the American Mathematical Society
17 Journal of Algebra
16 Manuscripta Mathematica
15 Compositio Mathematica
15 Mathematische Annalen
14 Annales de l’Institut Fourier
12 International Journal of Mathematics
11 Journal of Number Theory
11 Journal für die Reine und Angewandte Mathematik
11 Journal of the American Mathematical Society
10 Journal of Combinatorial Theory. Series A
9 Geometriae Dedicata
9 Inventiones Mathematicae
9 Journal of Pure and Applied Algebra
9 Michigan Mathematical Journal
9 Discrete & Computational Geometry
9 Geometry & Topology
8 European Journal of Mathematics
7 Communications in Algebra
7 Nagoya Mathematical Journal
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 European Journal of Combinatorics
6 Journal de Mathématiques Pures et Appliquées. Neuvième Série
6 Journal of Algebraic Combinatorics
6 Nuclear Physics, B, Proceedings Supplements
6 Journal of Mathematical Sciences (New York)
6 Transformation Groups
6 Advances in Geometry
6 Proceedings of the Steklov Institute of Mathematics
5 Journal of Mathematical Physics
5 Mathematical Proceedings of the Cambridge Philosophical Society
5 Proceedings of the Japan Academy. Series A
5 Journal of the European Mathematical Society (JEMS)
5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
5 Kyoto Journal of Mathematics
4 International Journal of Modern Physics A
4 Letters in Mathematical Physics
4 Mathematics of Computation
4 Beiträge zur Algebra und Geometrie
4 Fortschritte der Physik
4 Collectanea Mathematica
4 Mathematische Nachrichten
4 The Electronic Journal of Combinatorics
4 Annals of Combinatorics
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Modern Physics Letters A
3 Physics Letters. B
3 Theoretical and Mathematical Physics
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Le Matematiche
3 Mathematika
3 Memoirs of the American Mathematical Society
3 Annals of Global Analysis and Geometry
3 Linear Algebra and its Applications
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Izvestiya: Mathematics
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 Forum of Mathematics, Sigma
3 Research in the Mathematical Sciences
2 Discrete Mathematics
2 Rocky Mountain Journal of Mathematics
2 Arkiv för Matematik
2 Reviews in Mathematical Physics
2 Acta Mathematica
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Canadian Journal of Mathematics
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 Bulletin of the Korean Mathematical Society
2 Journal of Symbolic Computation
2 SIAM Journal on Discrete Mathematics
2 Documenta Mathematica
2 Acta Mathematica Sinica. English Series
2 Communications in Contemporary Mathematics
2 Algebra & Number Theory
2 Science China. Mathematics
2 EMS Surveys in Mathematical Sciences
2 Complex Manifolds
1 American Mathematical Monthly
...and 67 more Serials
all top 5

Cited in 43 Fields

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

Citations by Year

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