Finite groups, smooth invariants, and isolated quotient singularities
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929597294051328 |
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| author | Braun, Amiram |
| author_facet | Braun, Amiram |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15593 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite groups, smooth invariants, and isolated quotient singularities Braun, Amiram Commutative Algebra Algebraic Geometry Representation Theory 13A50, 14B05, 14J17, 14L30 (Primary) 14L24 (Secondary) 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. |
| title | Finite groups, smooth invariants, and isolated quotient singularities |
| topic | Commutative Algebra Algebraic Geometry Representation Theory 13A50, 14B05, 14J17, 14L30 (Primary) 14L24 (Secondary) |
| url | https://arxiv.org/abs/2308.15593 |