The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings

Abstract

Given a projective scheme $X$ over a field $k$, an automorphism $\ddot{I}ƒ$ of $X$, and a $\ddot{I}ƒ$-ample invertible sheaf $L$, one may form the twisted homogeneous coordinate ring $B=B(X,L,\ddot{I}ƒ)$, one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum of $B$, as well as that of other closely related algebras such as skew and skew-Laurent extensions of commutative algebras. Over an algebraically closed, uncountable field $k$ of characteristic zero, we prove that that the primitive ideals of $B$ are characterized by the usual Dixmier-Moeglin conditions whenever the dimension of $X$ is no more than 2.

34 pages