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Separating invariants and local cohomology

Dufresne, Emilie; Jeffries, Jack

Authors

Emilie Dufresne

Jack Jeffries



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.

Journal Article Type Article
Publication Date Jan 31, 2015
Journal Advances in Mathematics
Print ISSN 0001-8708
Electronic ISSN 1090-2082
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 270
APA6 Citation Dufresne, E., & Jeffries, J. (2015). Separating invariants and local cohomology. Advances in Mathematics, 270, https://doi.org/10.1016/j.aim.2014.11.003
DOI https://doi.org/10.1016/j.aim.2014.11.003
Keywords Invariant theory, separating invariants, local cohomology, arrangements of linear subspaces, simplicial homology, poset topology.
Publisher URL http://www.sciencedirect.com/science/article/pii/S0001870814003788
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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