Preprints of Prof. Batyrev

• Combinatorial aspects of mirror symmetry
  March 2007
  with: Benjamin Nill



• Lattice polytopes with a given $h^*$-polynomial
  February 2006
  Algebraic and geometric combinatorics, 1--10, Contemp. Math., 423, Amer. Math. Soc., Providence, RI, 2006.
  



• Multiples of lattice polytopes without interior lattice points
  February 2006
  Mosc. Math. J. 7 (2007), no. 2, 195--207
  with: Benjamin Nill



• Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
  May 2005
  Mirror symmetry. V, 255--270, AMS/IP Stud. Adv. Math., 38, Amer. Math. Soc., Providence, RI, 2006.
  with: Maximilian Kreuzer



• The Cox ring of a Del Pezzo surface
  September 2003
  Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), 85--103, Progr. Math., 226, Birkhäuser Boston, Boston, MA, 2004.
  with: Oleg N. Popov



• Mixed toric residues and Calabi-Yau complete intersections
  June 2002
  Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001), 3--26, Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI, 2003
  with: Evgeny N. Materov



• Toric Residues and Mirror Symmetry
  March 2002
  Mosc. Math. J. 2 (2002), no. 3, 435--475
  with: Evgeny N. Materov



• Canonical abelianization of finite group actions
  September 2000



• Einstein-Kaehler Metrics on Symmetric Toric Fano Manifolds
  January 1999
  J. Reine Angew. Math. 512 (1999), 225--236.
  with: Elena N. Selivanova



• Mirror Symmetry and Toric Degenerations of Partial Flag Manifolds
  March 1998
  Acta Math. 184 (2000), no. 1, 1--39
  with: Ionut Ciocan-Fontanine, Bumsig Kim, Duco van Straten



• Non-Archimedian integrals and stringy Euler numbers of log terminal pairs
  March 1998
  J. Eur. Math. Soc. (JEMS) 1 (1999), no. 1, 5--33
  
  
• On the Classification of Toric Fano 4-folds
  January 1998
  J. Math. Sci. (New York) 94 (1999), no. 1, 1021--1050
  
  
• Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds
  December 1997
  The Fano Conference, 109--122, Univ. Torino, Turin, 2004.
  
  
• Tamagawa numbers of polarized algebraic varieties
  November 1997
  Astérisque No. 251 (1998), 299--340
  with: Yu. Tschinkel



• Stringy Hodge numbers and Virasoro algebra
  November 1997
  Math. Res. Lett. 7 (2000), no. 2-3, 155--164
  
  
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
  November 1997
  Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), 1--32, World Sci. Publishing, River Edge, NJ, 1998.
  
  
• Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
  October 1997
  Nuclear Phys. B 514 (1998), no. 3, 640--666.
  with: Ionut Ciocan-Fontanine, Bumsig Kim, Duco van Straten



• Birational Calabi--Yau n-folds have equal Betti numbers
  October 1997
  New trends in algebraic geometry (Warwick, 1996), 1--11, London Math. Soc. Lecture Note Ser., 264, Cambridge Univ. Press, Cambridge, 1999
  
  
• Height Zeta Functions of Toric Varieties
  June 1996
  J. Math. Sci. 82 (1996), no. 1, 3220--3239
  with: Yuri Tschinkel



• Rational points on some Fano cubic bundles
  Februar 1996
  C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 1, 41--46
  with: Yuri Tschinkel



• Manin's conjecture for toric varieties
  October 1995
  J. Algebraic Geom. 7 (1998), no. 1, 15--53
  with: Yuri Tschinkel



• Mirror duality and string-theoretic Hodge numbers
  September 1995
  Invent. Math. 126 (1996), no. 1, 183--203
  with: Lev A. Borisov



• On Calabi-Yau Complete Intersections in Toric Varieties
  December 1994
  Higher-dimensional complex varieties (Trento, 1994), 39--65, de Gruyter, Berlin, 1996
  with: Lev A. Borisov



• Rational Points of Bounded Height on Compactifications of Anisotropic Tori
  November 1994
  Internat. Math. Res. Notices 1995, no. 12, 591--635
  with: Yuri Tschinkel



• Strong McKay Correspondence, String-theoretic Hodge Numbers and Mirror Symmetry
  October 1994
  Topology 35 (1996), no. 4, 901--929
  with: Dimitrios I. Dais



• Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
  Februar 1994
  Mirror symmetry, II, 71--86, AMS/IP Stud. Adv. Math., 1, Amer. Math. Soc., Providence, RI, 1997
  with: Lev A. Borisov



• Quantum Cohomology Rings of Toric Manifolds
  October 1993
  Astérisque No. 218 (1993), 9--34
  
  
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
  October 1993
  J. Algebraic Geom. 3 (1994), no. 3, 493--535
  
  
• Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau Complete Intersections in Toric Varieties
  July 1993
  Comm. Math. Phys. 168 (1995), no. 3, 493--533
  with: Duco van Straten



• On the Hodge Structure of Projective Hypersurfaces in Toric Varieties
  June 1993
  Duke Math. J. 75 (1994), no. 2, 293--338
  with: David A. Cox




Some other publications:




• Batyrev, Victor V. Mirror symmetry and toric geometry Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 239--248



• Batyrev, Victor V. Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori. Duke Math. J. 69 (1993), no. 2, 349--409



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



• Batyrev, Victor V. On the classification of smooth projective toric varieties. Tohoku Math. J. (2) 43 (1991), no. 4, 569--585



• Batyrev, V. V.; Manin, Yu. I. Sur le nombre des points rationnels de hauteur borné des variétés algébriques. (French) [On the number of rational points of bounded height of algebraic varieties] Math. Ann. 286 (1990), no. 1-3, 27--43.



• Batyrev, V. V.; Mel'nikov, D. A. A theorem on nonextendability of toric varieties. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1986, no. 3, 20--24, 118



• Batyrev, V. V. Some numerical characteristics of multidimensional Fano varieties. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 2, 445--459, 463



• Batyrev, V. V. Boundedness of the degree of multidimensional toric Fano varieties. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1982, no. 1, 22--27, 76--77.



• Batyrev, V. V. Toric Fano threefolds. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), no. 4, 704--717, 927.



• Batyrev, V. V. Rational equivalence and K-theory on toric varieties. (Russian) Algebra, logic and number theory (Russian), 15--17, Moskov. Gos. Univ., Moscow, 1986