Birational smooth minimal models have equal Hodge numbers in all dimensions
Number Theory
2007-05-23 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0209269,
title = {Birational smooth minimal models have equal Hodge numbers in all dimensions},
author = {Tetsushi Ito},
journal= {arXiv preprint arXiv:math/0209269},
year = {2007}
}
Comments
14 pages, AMS LaTeX, remarks and references added, to appear in the Proceedings of Calabi-Yau Varieties and Mirror Symmetry