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Batyrev, Victor Vadimovich
Total publications: 57 (57)
in MathSciNet: 54 (54)
in zbMATH: 45 (45)
in Web of Science: 6 (6)
in Scopus: 16 (16)
Cited articles: 29
Citations: 930
Presentations: 18

Number of views:
This page:4375
Abstract pages:3674
Full texts:653
References:450
Batyrev, Victor Vadimovich
Professor
Doctor of physico-mathematical sciences
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords: algebraic varieties
UDC: 512.7, 513.6
MSC: 14M25, 14J45, 52B20

Subject:

Toric and spherical varieties, rational points on algebraic varieties, Fano varieties, Calabi-Yau varieties, mirror symmetry
   
Main publications:
  1. Batyrev, V. V. and Manin, Yu. I., “Sur le nombre des points rationnels de hauteur borné des variétés algébriques”, Math. Ann., 286:1-3 (1990), 27–43
  2. Batyrev, Victor V., “Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori”, Duke Math. J., 69:2 (1993), 349–409
  3. Batyrev, Victor V., “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, J. Algebraic Geom., 3:3 (1994), 493–535
  4. Batyrev, Victor V. and Tschinkel, Yuri, “Manin's conjecture for toric varieties”, J. Algebraic Geom., 7:1 (1998), 15–53
  5. Batyrev, Victor V., “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, J. Eur. Math. Soc., 1:1 (1999), 5–33

https://www.mathnet.ru/eng/person25047
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/219978

List of publications:
| scientific publications | by years | by types | by times cited | common list |


Citations (Crossref Cited-By Service + Math-Net.Ru)

   2019
1. V. V. Batyrev, K. Schaller, “Stringy $E$-functions of canonical toric Fano threefolds and their applications”, Izv. Math., 83:4 (2019), 676–697  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus

   2017
2. Victor Batyrev, The stringy Euler number of Calabi-Yau hypersurfaces in toric varieties and the Mavlyutov duality, 2017 (Published online) , 35 pp., arXiv: 1707.02602
3. V. Batyrev, K. Schaller, “Stringy Chern classes of singular toric varieties and their applications”, Commun.Num.Theor.Phys., 11 (2017), 1–40  crossref  mathscinet  zmath  scopus 4
4. V. Batyrev, G. Gagliardi, “On the algebraic stringy Euler number”, Proc. Amer. Math. Soc., 145 (2017), 1–13 (to appear)  crossref  mathscinet  isi  scopus

   2016
5. V. Batyrev, A. Moreau, Satellites of spherical subgroups, 2016 (Published online) , 39 pp., arXiv: 1610.07377

   2013
6. V. Batyrev, A. Moreau, “The arc space of horospherical varieties and motivic integration”, Compositio Mathematica, 149:8 (2013), 1327–1352  crossref  mathscinet  zmath  scopus 10
7. V. Batyrev, M. Kreuzer, “Conifold degenerations of Fano 3-folds as hypersurfaces in toric varieties”, Strings, gauge fields, and the geometry behind, World Sci. Publ., Hackensack, NJ, 2013, 187–212  mathscinet
8. V. Batyrev, J. Hofscheier, Lattice polytopes, finite abelian subgroups in $\operatorname{SL}(n)$ and coding theory, 2013 (Published online) , 18 pp., arXiv: 1309.5312  zmath

   2012
9. K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held April 15–21, 2012.”, Oberwolfach Reports, 9:2 (2012), 1231–1306  crossref  mathscinet  zmath

   2011
10. V. Batyrev, M. Blume, “On generalisations of Losev-Manin moduli spaces for classical root systems”, Pure Appl. Math. Q., 7:4 (2011), 1053–1084  crossref  mathscinet  zmath 9
11. V. Batyrev, M. Blume, “The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces”, The Tohoku Mathematical Journal. Second Series, 63:4 (2011), 581–604  crossref  mathscinet  zmath  scopus 13

   2010
12. Victor Batyrev, Dorothee Juny, “Classification of Gorenstein toric Del Pezzo varieties in arbitrary dimension”, Mosc. Math. J., 10:2 (2010), 285–316  mathnet  crossref  mathscinet  isi 11
13. V. Batyrev, M. Kreuzer, “Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions”, Advances in Theoretical and Mathematical Physics, 14:3 (2010), 879–898  crossref  mathscinet  zmath  scopus 22
14. V. Batyrev, J. Hofscheier, A generalization of a theorem of G. K. White, 2010 (Published online) , 12 pp., arXiv: 1004.3411

   2009
15. K. Altmann, V. Batyrev, Y. Karshon, “Toric geometry. Abstracts from the workshop held January 4th – January 10th, 2009.”, Oberwolfach Reports, 6:1 (2009), 5–74  crossref  mathscinet  zmath

   2008
16. V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646  mathnet  crossref  mathscinet  zmath  isi 8
17. V. Batyrev, B. Nill, “Combinatorial aspects of mirror symmetry”, Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, Contemp. Math., 452, Amer. Math. Soc., Providence, RI, 2008, 35–66  crossref  mathscinet  zmath 31

   2007
18. V. Batyrev, B. Nill, “Multiples of lattice polytopes without interior lattice points”, Mosc. Math. J., 7:2 (2007), 195–207  mathnet  crossref  mathscinet  zmath  isi 37

   2006
19. Victor Batyrev, “Lattice polytopes with a given $h^*$-polynomial”, Algebraic and geometric combinatorics, 423, Amer. Math. Soc., Providence, RI, 2006, 1–10 (to appear)  mathnet  crossref  mathscinet  zmath
20. V. Batyrev, M. Kreuzer, “Integral cohomology and mirror symmetry for Calabi-Yau 3-folds”, Mirror symmetry. V, AMS/IP Stud. Adv. Math., 38, Amer. Math. Soc., Providence, RI, 2006, 255–270  crossref  mathscinet  zmath 4
21. K. Altmann, V. Batyrev, B. Tessier, “Report 5/2006: Convex and Algebraic Geometry (January 29th – February 4th, 2006)”, Oberwolfach Reports, 3:1 (2006), 253–316  crossref  mathscinet  zmath 1

   2004
22. Victor Batyrev, “Toric degenerations of Fano varieties and constructing mirror manifolds”, The Fano Conference, Univ. Torino, Turin, 2004, 109–122  mathscinet  zmath
23. V. Batyrev, O. Popov, “The Cox ring of a del Pezzo surface”, Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), Progr. Math., 226, Birkhäuser Boston, Boston, MA, 2004, 85–103  crossref  mathscinet  zmath 33

   2003
24. V. Batyrev, E. Materov, “Mixed toric residues and Calabi-Yau complete intersections”, Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001), Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI, 2003, 3–26  mathscinet  zmath

   2002
25. V. V. Batyrev, E. N. Materov, “Toric residues and mirror symmetry”, Mosc. Math. J., 2:3 (2002), 435–475  mathnet  crossref  mathscinet  zmath  isi  elib 16

   1996
26. V. V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, J. Math. Sci., 82:1 (1996), 3220–3239  mathnet  crossref  mathscinet  zmath

   2000
27. Victor Batyrev, “Stringy Hodge numbers and Virasoro algebra”, Mathematical Research Letters, 7:2-3 (2000), 155–164  mathscinet  zmath
28. V. Batyrev, I. Ciocan-Fontanine, B. Kim, D. van Straten, “Mirror symmetry and toric degenerations of partial flag manifolds”, Acta Mathematica, 184:1 (2000), 1–39  crossref  mathscinet  zmath  scopus 68
29. Victor Batyrev, Canonical abelianization of finite group actions, 2000 (Published online) , 4 pp., arXiv: math/0009043

   1999
30. V. Batyrev, E. Selivanova, “Einstein-Kähler metrics on symmetric toric Fano manifolds”, J. Reine Angew. Math., 512 (1999), 225–236  crossref  mathscinet  zmath  scopus 20
31. Victor Batyrev, “Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs”, Journal of the European Mathematical Society, 1:1 (1999), 5–33  crossref  mathscinet 57
32. Victor Batyrev, “Birational Calabi-Yau $n$-folds have equal Betti numbers”, New trends in algebraic geometry (Warwick, 1996), London Math. Soc. Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999, 1–11  mathscinet  zmath

   1998
33. Victor Batyrev, “Mirror symmetry and toric geometry”, Documenta Mathematica, 1998, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 239–248  mathscinet  zmath
34. V. Batyrev, Ju. Tschinkel, “Manin's conjecture for toric varieties”, Journal of Algebraic Geometry, 7:1 (1998), 15–53  mathscinet  zmath
35. Victor Batyrev, “Stringy Hodge numbers of varieties with Gorenstein canonical singularities”, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publ., River Edge, NJ, 1998, 1–32  mathscinet  zmath
36. V. Batyrev, I. Ciocan-Fontanine, B. Kim, D. van Straten, “Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians”, Nuclear Phys. B, 514:3 (1998), 640–666  crossref  mathscinet  zmath  adsnasa  scopus 62
37. V. Batyrev, Yu. Tschinkel, “Tamagawa numbers of polarized algebraic varieties”, Nombre et répartition de points de hauteur bornée (Paris, 1996), Astérisque, 251, Soc. Math. France, 1998, 299–340  mathscinet  zmath

   1997
38. V. Batyrev, L. Borisov, “Dual cones and mirror symmetry for generalized Calabi-Yau manifolds”, Mirror symmetry, II, Amer. Math. Soc., Providence, RI, 1997, 71–86  mathscinet

   1996
39. V. Batyrev, Yu. Tschinkel, “Rational points on some Fano cubic bundles”, C. R. Acad. Sci. Paris Sér. I Math., 323:1 (1996), 41–46  mathscinet  zmath
40. V. Batyrev, D. Dais, “Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry”, Topology, 35:4 (1996), 901–929  crossref  mathscinet  zmath  scopus 79
41. V. Batyrev, L. Borisov, “Mirror duality and string-theoretic Hodge numbers”, Invent. Math., 126:1 (1996), 183–203  crossref  mathscinet  zmath  adsnasa  scopus 61
42. V. Batyrev, L. Borisov, “On Calabi-Yau complete intersections in toric varieties”, Higher-dimensional complex varieties (Trento, 1994), de Gruyter, Berlin, 1996, 39–65  mathscinet  zmath
43. V. Batyrev, Yu. Tschinkel, “Height zeta functions of toric varieties”, Journal of Mathematical Sciences, 82:1 (1996), 3220–3239  crossref  mathscinet  zmath  scopus 26

   1995
44. V. Batyrev, D. van Straten, “Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties”, Comm. Math. Phys., 168:3 (1995), 493–533  crossref  mathscinet  zmath  adsnasa  scopus 69
45. V. Batyrev, Yu. Tschinkel, “Rational points on toric varieties”, Number theory (Halifax, NS, 1994), CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI, 1995, 39–48  mathscinet  zmath
46. V. Batyrev, Yu. Tschinkel, “Rational points of bounded height on compactifications of anisotropic tori”, Internat. Math. Res. Notices, 1995, no. 12, 591–635  crossref  mathscinet  zmath  scopus 31

   1994
47. Victor Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties”, Journal of Algebraic Geometry, 3:3 (1994), 493–535  mathscinet  zmath
48. V. Batyrev, D. Cox, “On the Hodge structure of projective hypersurfaces in toric varieties”, Duke Math. J., 75:2 (1994), 293–338  crossref  mathscinet  zmath  scopus 96

   1993
49. Victor Batyrev, “Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori”, Duke Math. J., 169 (1993), 349–409  mathscinet
50. Victor Batyrev, “Quantum cohomology rings of toric manifolds”, Journées de Géométrie Algébrique d'Orsay (Orsay, 1992), Astérisque, 218, Soc. Math. France, 1993, 9–34  mathscinet  zmath

   1992
51. Victor Batyrev, “The cone of effective divisors of threefolds”, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989), Contemp. Math., 131, Amer. Math. Soc., Providence, RI, 1992, 337–352  mathscinet

   1991
52. Victor Batyrev, “On the classification of smooth projective toric varieties”, The Tohoku Mathematical Journal. Second Series, 43:4 (1991), 569–585  mathscinet  zmath

   1990
53. V. Batyrev, Ju. Manin, “Sur le nombre des points rationnels de hauteur borné des variétés algébriques”, Math. Ann., 286:1-3 (1990), 27–43  crossref  mathscinet  zmath  scopus 98

   1986
54. V. V. Batyrev, D. A. Melnkiov, “A theorem on nonextendability of toric varieties”, Moscow Univ. Math. Bull., 41:3 (1986), 23–27 (to appear)  mathnet  mathscinet  mathscinet  zmath
55. V. V. Batyrev, “On some numerical characteristics of multidimensional Fano varieties”, Math. USSR-Izv., 26:2 (1986), 423–435  mathnet  crossref  mathscinet  zmath

   1982
56. Victor Batyrev, “Boundedness of the degree of multidimensional toric Fano varieties”, Moscow Univ. Math. Bull., 37:1 (1982), 28–33  mathnet  mathscinet  mathscinet  zmath
57. V. V. Batyrev, “Toroidal Fano 3-folds”, Math. USSR-Izv., 19:1 (1982), 13–25  mathnet  crossref  mathscinet  zmath

Presentations in Math-Net.Ru
1. Глобальное сглаживание минимальных гиперповерхностей Калаби–Яу в $4$-мерных торических многообразиях
V. V. Batyrev
Memorial conference dedicated to the memory of A. N. Parshin
November 12, 2024 11:30   
2. Towards birational classification of 3-folds determined by 4-dimensional empty lattice simplices
Victor Batyrev
Conference “Birational geometry and Fano varieties” dedicated to Yu.G. Prokhorov 60th anniversary
March 13, 2024 17:30   
3. О структурах Ходжа $CM$-типа, связанных с целочисленными симплексами
V. V. Batyrev
Conference on algebra, algebraic geometry, and number theory on the occasion of academician Igor Rostislavovich Shafarevich 100th birthday
June 6, 2023 11:00   
4. The Mori program for non-degenerate toric hypersurfaces of arbitrary dimension
V. V. Batyrev
Iskovskikh Seminar
March 9, 2023 16:45
5. Целочисленные многогранники и высотные функции на рациональных точках алгебраических торов
V. V. Batyrev
One-Day Conference Dedicated to the Memory of V. A. Iskovskikh
December 27, 2022 11:00   
6. Minimal models of non-degenerate toric hypersurfaces
V. V. Batyrev
Algebra and geometry: conference on the occasion of V.S. Kulikov 70th birthday
May 24, 2022 15:30   
7. Variations on the theme of classical discriminant
V. V. Batyrev
Multidimensional Residues and Tropical Geometry
June 16, 2021 12:00   
8. Stringy Euler numbers of toric Calabi-Yau hypersurfaces
Victor Batyrev
Iskovskikh Seminar
May 28, 2020 18:00   
9. Minimal models of surfaces with $p_g = 1; q = 0$ associated with canonical Fano $3$-polytopes
Victor Batyrev
"Birational Geometry and Fano varieties" dedicated to V. Iskovskikh
June 25, 2019 10:00   
10. Reflective polyhedra. The fourth lecture of mini-course "Combinatorial Mirror Symmetry"
V. V. Batyrev
Automorphic forms and their applications
October 2, 2017 18:00   
11. Toric varieties. The first lecture of mini-course "Combinatorial Mirror Symmetry"
V. V. Batyrev
Automorphic forms and their applications
September 25, 2017 18:00   
12. On virtual Poincaré polynomials of spherical varieties
V. V. Batyrev
Lie groups and invariant theory
March 22, 2017 16:45
13. Motivic integration on toric varieties and applications
V. Batyrev
International conference on algebraic geometry, complex analysis and computer algebra
August 7, 2016 09:40
14. The orbit space for the action of a maximal compact subgroup on a homogeneous complex spherical space
V. V. Batyrev
Lie groups and invariant theory
March 9, 2016 16:45
15. Неархимедовое интегрирование на алгебраических многообразиях и его приложения в бирациональной геометрии
V. V. Batyrev
Shafarevich Seminar
December 22, 2015 15:00
16. On a combinatorial classification of minimal quasi-homogeneous 3-folds with a $SL(2)\times G_m$-action
V. V. Batyrev
International conference "Geometry of Algebraic Varieties" dedicated to the memory of V. A. Iskovskikh
October 22, 2013 12:15   
17. Mavlyutov's mirror construction and string polytopes of homogeneous spaces
V. Batyrev
Weekly seminar of Laboratory of algebraic geometry
February 15, 2013 17:00
18. Квазиоднородные $\mathrm{SL}(2)$-многообразия с действием одномерного тора
V. Batyrev
Lie groups and invariant theory
September 23, 2009

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