Journal article
Separating invariants and local cohomology
- Abstract:
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Accepted manuscript, pdf, 385.2KB, Terms of use)
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- Publisher copy:
- 10.1016/j.aim.2014.11.003
Authors
- Publisher:
- Elsevier
- Journal:
- Advances in Mathematics More from this journal
- Volume:
- 270
- Pages:
- 565-581
- Publication date:
- 2014-11-27
- Acceptance date:
- 2014-11-04
- DOI:
- ISSN:
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0001-8708
- Keywords:
- Pubs id:
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pubs:652545
- UUID:
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uuid:9beaa11e-0f68-4ce2-bc0a-7d95dab17fdc
- Local pid:
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pubs:652545
- Deposit date:
-
2016-10-14
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier Inc
- Copyright date:
- 2014
- Notes:
-
This is an
accepted manuscript of a journal article published by Elsevier in Advances in Mathematics on 2014-11-27, available online: http://dx.doi.org/10.1016/j.aim.2014.11.003
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