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arXiv · 2308.15593

Finite groups, smooth invariants, and isolated quotient singularities

Amiram Braun
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Abstract

Let G < SL(V) be a finite group, V is finite dimensional over a field F, p=char F and S(V) is the symmetric algebra of V. We determine when the subring of G-invariants S(V)^G is a polynomial ring. As a consequence, we classify, if F is algebraically closed, all S(V)^G which are isolated singularities. We show that the completion of S(V)^G, at its unique graded maximal ideal, is isomorphic to the completion of S(W)^H, where (H,W) is a reduction mod p of a member of the Zassenhaus-Vincent-Wolf list of complex isolated quotient singularities.

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Amiram Braun. 2023-08-29. Finite groups, smooth invariants, and isolated quotient singularities. https://arxiv.org/abs/2308.15593

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