## Primitivity in twisted homogeneous coordinate rings

- Date: 09/25/2006

Jason Bell (Simon Fraser University)

University of British Columbia

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.

Algebraic Geometry Seminar 2006