On rings of invariants with rational singularities

Peskin, Barbara R.

doi:10.1090/S0002-9939-1983-0687629-0

On rings of invariants with rational singularities
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by Barbara R. Peskin PDF

Proc. Amer. Math. Soc. 87 (1983), 621-626 Request permission

Abstract:

Let $S$ be a noetherian local $k$-algebra and $G$ a finite group of $k$-automorphisms of $S$. If char $k = 0$ and $S$ has a rational singularity, then the invariant ring $R = {S^G}$ does also. However, if char $k \ne 0$, this is rarely true. We examine conditions on wild group actions in dimension two which ensure that the singularity of $R$ is rational. In particular, we develop a criterion in terms of the minimality of ${H^1}(G,S)$.

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