On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

Abstract

AbstractWe prove dimension formulas for the cotangent spaces T 1 and T 2 for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity X does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term c (X ) is zero for rational determinantal surface singularities. In particular our result implies that c (X ) is zero for Riemenschneiders quasi‐determinantal rational surface singularities, and this also generalizes results for quotient singularities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)