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Stringy Hodge numbers of varieties with Gorenstein canonical singularities. (English) Zbl 0963.14015

Saito, M.-H. (ed.) et al., Integrable systems and algebraic geometry. Proceedings of the 41st Taniguchi symposium, Kobe, Japan, June 30-July 4, 1997, and in Kyoto, Japan, July 7-11 1997. Singapore: World Scientific. 1-32 (1998).
Summary: 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 \(\mathbb{Q}\)-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 the appendix (pp. 17-32) we explain non-Archimedean 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.
For the entire collection see [Zbl 0949.00022].

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14B05 Singularities in algebraic geometry
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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