On the Castelnuovo-Mumford regularity of rings of polynomial invariants

Peter Symonds

doi:http://doi.org/10.4007/annals.2011.174.1.14

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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On the Castelnuovo-Mumford regularity of rings of polynomial invariants

Abstract

Authors