On the Castelnuovo-Mumford regularity of rings of polynomial invariants

Pages 499-517 from Volume 174 (2011), Issue 1 by Peter Symonds

Abstract

We show that when a group acts on a polynomial ring over a field the ring of invariants has Castelnuovo-Mumford regularity at most zero. As a consequence, we prove a well-known conjecture that the invariants are always generated in degrees at most $n(|G|-1)$, where $n >1$ is the number of polynomial generators and $|G|>1$ is the order of the group. We also prove some other related conjectures in invariant theory.

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Keywords
, , , , ,
DOI
http://doi.org/10.4007/annals.2011.174.1.14
MR
2811605
Zbl
05960708
Milestones
Received: 10 July 2009
Accepted: 10 December 2010
Published online: 1 July 2011

Authors

Peter Symonds

School of Mathematics
University of Manchester
Oxford Road
Manchester M13 9PL
United Kingdom