Noncommutative ampleness for multiple divisors

JOURNAL OF ALGEBRA

卷:265

Article

Keeler, DS

关键词: vanishing theorems;    invertible sheaves;    noetherian graded rings;    noncommutative projective geometry;   

DOI  :  10.1016/S0021-8693(03)00126-1

来源: Elsevier

【 摘 要 】

The twisted homogeneous coordinate ring is one of the basic constructions of the noncommutative projective geometry of Artin, Van den Bergh, and others. Chan generalized this construction to the multi-homogeneous case, using a concept of right ampleness for a finite collection of invertible sheaves and automorphisms of a projective scheme. From this he derives that certain multihomogeneous rings, such as tensor products of twisted homogeneous coordinate rings, are right noetherian. We show that right and left ampleness are equivalent and that there is a simple criterion for such ampleness. Thus we find under natural hypotheses that multi-homogeneous coordinate rings are noetherian and have integer GK-dimension. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free