Stringy Chern classes of toric varieties and their applications

Stringy Chern classes of singular projective algebraic varieties can be defined by some explicit formulas using a resolution of singularities. It is important that the output of these formulas does not depent on the choice of a resolution. The proof of this independence is based on the nonarchimedean motivic integration. The purpose of the talk is to explain a combinatorial computation of stringy Chern classes for singular toric varieties. As an application one obtains combinatorial formulas for the intersection numbers of stringy Chern classes with toric Cartier divisors and some interesting combinatorial identities for convex lattice polytopes.