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

Trond Stolen Gustavsen
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Abstract

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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Trond Stolen Gustavsen. 2003-12-14. On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle. https://arxiv.org/abs/math/0312278

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