Communications in Number Theory and Physics

Volume 11 (2017)

Number 1

Stringy Chern classes of singular toric varieties and their applications

Pages: 1 – 40



Victor Batyrev (Mathematisches Institut, Universität Tübingen, Germany)

Karin Schaller (Mathematisches Institut, Universität Tübingen, Germany)


Let $X$ be a normal projective $\mathbb{Q}$-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in $X$ via the total stringy Chern class of $X$. This formula is motivated by its applications to mirror symmetry for Calabi–Yau complete intersections in toric varieties.We compute stringy Chern classes and give a combinatorial interpretation of the stringy Libgober–Wood identity for arbitrary projective $\mathbb{Q}$-Gorenstein toric varieties. As an application we derive a new combinatorial identity relating $d$-dimensional reflexive polytopes to the number $12$ in dimension $d \geq 4$.

Received 26 July 2016

Published 16 June 2017