School of Mathematical Sciences

On the Castelnuovo-Mumford Regularity of Rings of Polynomial Invariants menu

On the Castelnuovo-Mumford Regularity of Rings of Polynomial Invariants

Speaker: 
Peter Symonds
(Manchester)
Date/Time: 
Mon, 26/10/2009 - 16:30
Room: 
M103
Seminar series: 

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.

The proof is a mixture of commutative algebra and representation theory.