Naive noncommutative blowups at zero-dimensional schemes

JOURNAL OF ALGEBRA

卷:318

Article

Rogalski, D.¹  Stafford, J. T.² 

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

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

DOI  :  10.1016/j.jalgebra.2007.02.017

来源: Elsevier

【 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.

【 授权许可】

Free