Separating invariants and local cohomology

Dufresne, Emilie; Jeffries, Jack

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.

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

• Journal Article Type: Article
• Acceptance Date: Nov 4, 2014
• Online Publication Date: Nov 27, 2014
• Publication Date: Jan 31, 2015
• Deposit Date: Oct 9, 2017
• Publicly Available Date: Oct 9, 2017
• Journal: Advances in Mathematics
• Print ISSN: 0001-8708
• Electronic ISSN: 1090-2082
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 270
• 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.
• Public URL: https://nottingham-repository.worktribe.com/output/742046
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0001870814003788
• Contract Date: Oct 9, 2017