## Primitivity in twisted homogeneous coordinate rings

• Date: 09/25/2006
Lecturer(s):

Jason Bell (Simon Fraser University)

Location:

University of British Columbia

Topic:

Given a projective k-scheme X, an automorphism sigma of X and an
invertible sheaf L on X, one can form the twisted homogeneous
coordinate ring bigoplus_{nge 0} H0(X,L_n), where L_n=Lotimes
L^{sigma}otimes cdotsotimes L^{sigma^{n-1}. We study the question of
primitivity of such rings. A ring R is primitive if it has a maximal
left ideal which does not contain a nonzero two sided ideal. We show in
many cases that primitivity of twisted homogeneous coordinate rings is
equivalent to the quotient division ring having trivial centre and to
the ring having finitely many height one primes. This gives a
Dixmier-Moeglin correspondence for many classes of twisted homogeneous
coordinate rings.

Other Information:

Algebraic Geometry Seminar 2006