On the Topology of Birational Minimal Models

Abstract

We show that birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth minimal models share the same Betti numbers. Our methods indicate a link between $p$-adic measure and the minimal model theory.

arXiv comment17 pages, Plain TeX file. Reported in the Differential Geometry Seminar at Harvard University in November 1997. To appear in Journel of Differential Geometry