Cotangent cohomology of rational surface singularities

Abstract.

In this paper we show that the number of generators of the cotangent cohomology groups T _Y ⁿ, n≥2, is the same for all rational surface singularities Y of fixed multiplicity. For a large class of rational surface singularities, including quotient singularities, this number is also the dimension. For them we obtain an explicit formula for the Poincaré series P _Y (t)=∑dim Tⁿ _Y ·tⁿ. In the special case of the cone over the rational normal curve we give the multigraded Poincaré series.