Separating invariants and local cohomology
The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ri...
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| Format: | Article |
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Elsevier
2015
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| Online Access: | https://eprints.nottingham.ac.uk/47066/ |
| _version_ | 1848797459777585152 |
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| author | Dufresne, Emilie Jeffries, Jack |
| author_facet | Dufresne, Emilie Jeffries, Jack |
| author_sort | Dufresne, Emilie |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ring of invariants. We investigate the least possible cardinality of a separating set for a given G-action. Our main result is a lower bound that generalizes the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections. We find these bounds to be sharp in a wide range of examples. |
| first_indexed | 2025-11-14T20:04:13Z |
| format | Article |
| id | nottingham-47066 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:04:13Z |
| publishDate | 2015 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-470662020-05-04T16:59:44Z https://eprints.nottingham.ac.uk/47066/ Separating invariants and local cohomology Dufresne, Emilie Jeffries, Jack The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ring of invariants. We investigate the least possible cardinality of a separating set for a given G-action. Our main result is a lower bound that generalizes the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections. We find these bounds to be sharp in a wide range of examples. Elsevier 2015-01-31 Article PeerReviewed Dufresne, Emilie and Jeffries, Jack (2015) Separating invariants and local cohomology. Advances in Mathematics, 270 . pp. 565-581. ISSN 1090-2082 Invariant theory separating invariants local cohomology arrangements of linear subspaces simplicial homology poset topology. http://www.sciencedirect.com/science/article/pii/S0001870814003788 doi:10.1016/j.aim.2014.11.003 doi:10.1016/j.aim.2014.11.003 |
| spellingShingle | Invariant theory separating invariants local cohomology arrangements of linear subspaces simplicial homology poset topology. Dufresne, Emilie Jeffries, Jack Separating invariants and local cohomology |
| title | Separating invariants and local cohomology |
| title_full | Separating invariants and local cohomology |
| title_fullStr | Separating invariants and local cohomology |
| title_full_unstemmed | Separating invariants and local cohomology |
| title_short | Separating invariants and local cohomology |
| title_sort | separating invariants and local cohomology |
| topic | Invariant theory separating invariants local cohomology arrangements of linear subspaces simplicial homology poset topology. |
| url | https://eprints.nottingham.ac.uk/47066/ https://eprints.nottingham.ac.uk/47066/ https://eprints.nottingham.ac.uk/47066/ |