Tomohiro Okuma (Yamagata University)

Normal reduction numbers and cohomology of normal surface singularities

Abstract

Let (A,m) be the local ring of a normal surface singularity (V,o). Then the degree of the generators of the normalization of the Rees algebra associated to m-primary ideals in A is bounded by the normal reduction number of (V,o). This invariant can be defined in terms of cohomology of line bundles on a resolution space. In this talk, we introduce some fundamental results on the normal reduction number, and then explain upper-bounds and formulas for some special cases. This is a joint work in progress with Kei-ichi Watanabe and Ken-ichi Yoshida.