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Stringy Hodge numbers of varieties with Gorenstein canonical singularities

Victor V. Batyrev
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Abstract

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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BibTeXRIS

Victor V. Batyrev. 1998-03-16. Stringy Hodge numbers of varieties with Gorenstein canonical singularities. https://arxiv.org/abs/alg-geom/9711008

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