Non-commutative Mori contractions and $\PP^1$-bundles
| dc.creator | Chan, Daniel | |
| dc.creator | Nyman, Adam | |
| dc.date | 2009-04-10 | |
| dc.date.accessioned | 2026-07-07T13:02:28Z | |
| dc.date.available | 2026-07-07T13:02:28Z | |
| dc.description | We give a method for constructing maps from a non-commutative scheme to a commutative projective curve. With the aid of Artin-Zhang's abstract Hilbert schemes, this is used to construct analogues of the extremal contraction of a $K$-negative curve with self-intersection zero on a smooth projective surface. This result will hopefully be useful in studying Artin's conjecture on the birational classification of non-commutative surfaces. As a non-trivial example of the theory developed, we look at non-commutative ruled surfaces and, more generally, at non-commutative $\PP^1$-bundles. We show in particular, that non-commutative $\PP^1$-bundles are smooth, have well-behaved Hilbert schemes and we compute its Serre functor. We then show that non-commutative ruled surfaces give examples of the aforementioned non-commutative Mori contractions. | |
| dc.description | 49 pages | |
| dc.identifier | https://arxiv.org/abs/0904.1717 | |
| dc.identifier | http://arxiv.org/abs/0904.1717 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226461 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | 14A22; 16S38 | |
| dc.title | Non-commutative Mori contractions and $\PP^1$-bundles | |
| dc.type | text |