Stringy Chern classes of singular toric varieties and their applications

TL;DR

This paper derives a formula for stringy Chern classes of complete intersections in singular toric varieties, with applications to mirror symmetry and combinatorial identities involving reflexive polytopes.

Contribution

It introduces a new formula linking the stringy Chern classes of a variety and its complete intersections, expanding understanding of singular toric varieties and their invariants.

Findings

Derived a formula for total stringy Chern class of complete intersections

Provided a combinatorial interpretation of the stringy Libgober-Wood identity

Established a new combinatorial identity involving reflexive polytopes and the number 12

Abstract

Let X be a normal projective 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 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>3.