Blowing up non-commutative smooth surfaces
| dc.creator | Bergh, Michel Van den | |
| dc.date | 1998-09-21 | |
| dc.date.accessioned | 2026-07-07T05:26:05Z | |
| dc.date.available | 2026-07-07T05:26:05Z | |
| dc.description | In this paper we will think of certain abelian categories with favorable properties as non-commutative surfaces. We show that under certain conditions a point on a non-commutative surface can be blown up. This yields a new non-commutative surface which is in a certain sense birational to the original one. This construction is analogous to blowing up a Poisson surface in a point of the zero-divisor of the Poisson bracket. By blowing up $\le 8$ points in the elliptic quantum plane one obtains global non-commutative deformations of Del-Pezzo surfaces. For example blowing up six points yields a non-commutative cubic surface. Under a number of extra hypotheses we obtain a formula for the number of non-trivial simple objects on such non-commutative surfaces. | |
| dc.identifier | https://arxiv.org/abs/math/9809116 | |
| dc.identifier | http://arxiv.org/abs/math/9809116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77422 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16E40 | |
| dc.title | Blowing up non-commutative smooth surfaces | |
| dc.type | text |