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Birational smooth minimal models have equal Hodge numbers in all dimensions

Tetsushi Ito
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Abstract

This is a resume of the author's talk at the Worhshop on Arithmetic, Geometry and Physics around Calabi-Yau Varieties and Mirror Symmetry (July 23-29, 2001), the Fields Institute. The aim of this note is to prove that birational smooth minimal models over C have equal Hodge numbers in all dimensions by an arithmetic method. Our method is a refinement of the method of V. Batyrev and C.-L. Wang on Betti numbers who used p-adic integration and the Weil conjecture. Our ingredient is to use further arithmetic results such as the Chebotarev density theorem and p-adic Hodge theory.

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Tetsushi Ito. 2002-11-24. Birational smooth minimal models have equal Hodge numbers in all dimensions. https://arxiv.org/abs/math/0209269

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