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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On rings of invariants with rational singularities


Author: Barbara R. Peskin
Journal: Proc. Amer. Math. Soc. 87 (1983), 621-626
MSC: Primary 14L30; Secondary 14B05
MathSciNet review: 687629
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687629-0
PII: S 0002-9939(1983)0687629-0
Keywords: Wild group action, rational singularity
Article copyright: © Copyright 1983 American Mathematical Society