On the Castelnuovo-Mumford regularity of rings of polynomial invariants


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.


Peter Symonds

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