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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MRCLASS = {13A50 (13E15 20F29)},
MRNUMBER = {1249931},
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