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 polynomi...

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Bibliographic Details
Published in:Annals of mathematics 2011-07, Vol.174 (1), p.499-517
Main Author: Symonds, Peter
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
General mathematics
General, history and biography
Integers
Mathematical rings
Mathematical theorems
Mathematics
Polynomials
Sciences and techniques of general use
Subrings
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Summary: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.
ISSN:0003-486X
1939-8980
DOI:10.4007/annals.2011.174.1.14