ON THE COTANGENT COHOMOLOGY OF RATIONAL SURFACE SINGULARITIES WITH ALMOST REDUCED FUNDAMENTAL CYCLE

We prove dimension formulas for the cotangent spaces T1 and T2 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 generalise results for qoutient singularities