988 citations · 2k across the 45 of their papers we have counts for
16 papers · 1 filter
Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds
Victor V. Batyrev
For an arbitrary smooth n-dimensional Fano variety we introduce the notion of a small toric degeneration. Using small toric degenerations of Fano n-folds , we propose a gene…
Tamagawa numbers of polarized algebraic varieties
Victor V. Batyrev, Yu. Tschinkel
Let be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety defined over a number field. Denote by $N(V,{\cal L},B)…
Stringy Hodge numbers and Virasoro algebra
Victor V. Batyrev
Let be an arbitrary smooth -dimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes depends only on t…
Stringy Hodge numbers of varieties with Gorenstein canonical singularities
Victor V. Batyrev
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of st…
Conifold Transitions and Mirror Symmetry for Calabi-Yau Complete Intersections in Grassmannians
Victor V. Batyrev, Ionunt Ciocan-Fontanine, Bumsig Kim +1
In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of…
Birational Calabi--Yau n-folds have equal Betti numbers
Victor V. Batyrev
Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties…
Rational points on some Fano cubic bundles
Victor V. Batyrev, Yuri Tschinkel
We consider some families of smooth Fano hypersurfaces in given by a homogeneous polynomial of bidegree . For these varieties we o…
Manin's conjecture for toric varieties
Victor V. Batyrev, Yuri Tschinkel
We prove an asymptotic formula conjectured by Manin for the number of -rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth proje…
Mirror duality and string-theoretic Hodge numbers
Victor V. Batyrev, Lev A. Borisov
We prove in full generality the mirror duality conjecture for string-theoretic Hodge numbers of Calabi-Yau complete intersections in Gorenstein toric Fano varieties. The proof is b…
On Calabi-Yau Complete Intersections in Toric Varieties
Victor V. Batyrev, Lev A. Borisov
We investigate Hodge-theoretic properties of Calabi-Yau complete intersections of semi-ample divisors in -dimensional toric Fano varieties having at most Gorenstein sing…
Strong McKay Correspondence, String-theoretic Hodge Numbers and Mirror Symmetry
Victor V. Batyrev, Dimitrios I. Dais
In the revised version of the paper, we correct misprints and add some new statements.
Rational Points of Bounded Height on Compactifications of Anisotropic Tori
Victor V. Batyrev, Yuri Tschinkel
We investigate the analytic properties of the zeta-function associated with heights on equivariant compactifications of anisotropic tori over number fields. This allows to verify c…
Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
Victor V. Batyrev, Lev A. Borisov
We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension , where is a positive int…
Quantum Cohomology Rings of Toric Manifolds
Victor V. Batyrev
We compute the quantum cohomology ring of an arbitrary -dimensional smooth projective toric manifold associated with a fan . The multipl…
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
Victor V. Batyrev
We consider families consisting of complex -dimensional projective algebraic compactifications of -regular affine hypersurfaces defined by Laurent pol…
Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau Complete Intersections in Toric Varieties
Victor V. Batyrev, Duco van Straten
We formulate general conjectures about the relationship between the A-model connection on the cohomology of a -dimensional Calabi-Yau complete intersection of hypersurfa…