Naive noncommutative blowups at zero-dimensional schemes

[摘要] In an earlier paper [D.S. Keeler, D. Rogalski, J.T. Stafford, Naive noncommutative blowing up, Duke Math. J. 126 (2005) 491-546, MR 2120116], we defined and investigated the properties of the naive blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one naively blows up X at any suitably generic zero-dimensional subscheme Z. The resulting algebra A has a number of curious properties; for example it is noetherian but never strongly noetherian and the point modules are never parametrized by a projective scheme. This is despite the fact that the category of torsion modules in qgr-A is equivalent to the category of torsion coherent sheaves over X. These results are used in the companion paper [D. Rogalski, J.T. Stafford, A class of noncommutative projective surfaces, in press] to prove that a large class of noncommutative surfaces can be written as nave blowups. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] noncommutative projective geometry;noncommutative surfaces;noetherian graded rings;Naive blowing up