Ehrhart polynomials and stringy Betti numbers

Abstract

We study the connection between stringy Betti numbers of Gorenstein toric varieties and the generating functions of the Ehrhart polynomials of certain polyhedral regions. We use this point of view to give counterexamples to Hibi's conjecture on the unimodality of delta-vectors of reflexive polytopes.

8 pages; revised version: added reference to paper of Batyrev-Dais, combinatorial proof of Theorem 1.3 included; to appear in Math. Ann