Birational Calabi--Yau n-folds have equal Betti numbers

Abstract

Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number fields to prove that if X and Y are birational, they have the same Betti numbers.

AMS-LaTeX, 11 pages, to appear in in Proc. European Algebraic Geometry Conference (Warwick, 1996)