V. Batyrev

activity

19932024

most citedDual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

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

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5 papers · 1 filter

math.CO2013★ 5 cited

Lattice polytopes, finite abelian subgroups in $\SL(n,\C)$ and coding theory

Victor Batyrev, Johannes Hofscheier

We consider $d$ -dimensional lattice polytopes $Δ$ with $h^{*}$ -polynomial $h_{Δ}^{*} = 1 + h_{k}^{*} t^{k}$ for $1 < k < (d + 1) /2$ and relate them to some abelian subgroups of $\SL_{d+1}(\C)$ of order $…

math.CO2010★ 5 cited

A generalization of a theorem of G. K. White

Victor Batyrev, Johannes Hofscheier

An n-dimensional simplex Δ in \R^n is called empty lattice simplex if Δ\cap\Z^n is exactly the set of vertices of Δ. A theorem of G. K. White shows that if n=3 then any empty latti…

math.CO2007★ 2 cited

Combinatorial aspects of mirror symmetry

Victor Batyrev, Benjamin Nill

The purpose of this paper is to review some combinatorial ideas behind the mirror symmetry for Calabi-Yau hypersurfaces and complete intersections in Gorenstein toric Fano varietie…

math.CO2006

Lattice polytopes with a given $h^{*}$ -polynomial

Victor Batyrev

Let $Δ \subset R^{n}$ be an $n$ -dimensional lattice polytope. It is well-known that $h_{Δ}^{*} (t) := (1 - t)^{n + 1} \sum_{k \geq 0} ∣ k Δ \cap Z^{n} ∣ t^{k}$ is a polynomial of degree $d \leq n$ …