Stringy Hodge numbers of varieties with Gorenstein canonical singularities

Details Stringy Hodge numbers of varieties with Gorenstein canonical singularities Stringy Hodge numbers of varieties with Gorenstein canonical singularities

1997-11-06

arxiv.org/abs/alg-geom/9711008v2

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, AMSLaTeX, to appear in the Proceedings of Taniguchi Symposium 1997,"Integrable Systems and Algebraic Geometry, Kobe/

Scientific paper

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.

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