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

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

2003-12-14

arxiv.org/abs/math/0312278v1

Mathematics

Algebraic Geometry

11 pages, one figure

Scientific paper

We 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 generalise results for qoutient singularities.

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