Stringy Hodge numbers of varieties with Gorenstein canonical singularities
Abstract
Description
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions and compute them explicitly for arbitrary Q-Gorenstein toric varieties. Using stringy E-functions, we propose a general method to define stringy Hodge numbers for projective algebraic varieties with at worst Gorenstein canonical singularities. This allows us to formulate the topological mirror duality test for arbitrary Calabi-Yau varieties with canonical singularities. In Appendix we explain non-Archimedian integrals over spaces of arcs. We need these integrals for the proof of the main technical statement used in the definition of stringy Hodge numbers.
26 pages, AMSLaTeX, to appear in the Proceedings of Taniguchi Symposium 1997,"Integrable Systems and Algebraic Geometry, Kobe/Kyoto"
26 pages, AMSLaTeX, to appear in the Proceedings of Taniguchi Symposium 1997,"Integrable Systems and Algebraic Geometry, Kobe/Kyoto"