988 citations · 2k across the 45 of their papers we have counts for
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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…