Separating invariants and local cohomology

Dufresne, Emilie and Jeffries, Jack (2015) Separating invariants and local cohomology. Advances in Mathematics, 270 . pp. 565-581. ISSN 1090-2082

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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.

Item Type: Article
Keywords: Invariant theory, separating invariants, local cohomology, arrangements of linear subspaces, simplicial homology, poset topology.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1016/j.aim.2014.11.003
Depositing User: Dufresne, Emilie
Date Deposited: 09 Oct 2017 10:29
Last Modified: 13 Oct 2017 09:11
URI: http://eprints.nottingham.ac.uk/id/eprint/47066

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