Naive noncommutative blowups at zero-dimensional schemes
| dc.creator | Rogalski, D. | |
| dc.creator | Stafford, J. T. | |
| dc.date | 2006-12-21 | |
| dc.date.accessioned | 2026-07-07T07:36:38Z | |
| dc.date.available | 2026-07-07T07:36:38Z | |
| dc.description | In an earlier paper (D. S. Keeler, D. Rogalski, and J. T. Stafford, ``Naive noncommutative blowing up,'' Duke Math. J., 126 (2005), 491-546), 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 the quotient category qgr A is equivalent to the category of torsion coherent sheaves over X. These results are used in the companion paper ``A class of noncommutative projective surfaces'' to prove that a large class of noncommutative surfaces can be written as naive blowups. | |
| dc.identifier | https://arxiv.org/abs/math/0612658 | |
| dc.identifier | http://arxiv.org/abs/math/0612658 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120498 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 14A22, 16P40 | |
| dc.title | Naive noncommutative blowups at zero-dimensional schemes | |
| dc.type | text |