Secant varieties and Hirschowitz bound on vector bundles over a curve
| dc.creator | Choe, Insong | |
| dc.creator | Hitching, George H. | |
| dc.date | 2009-05-11 | |
| dc.date | 2009-05-15 | |
| dc.date.accessioned | 2026-07-07T13:14:53Z | |
| dc.date.available | 2026-07-07T13:14:53Z | |
| dc.description | For a vector bundle V over a curve X of rank n and for each integer r in the range 1 \le r \le n-1, the Segre invariant s_r is defined by generalizing the minimal self-intersection number of the sections on a ruled surface. In this paper we generalize Lange and Narasimhan's results on rank 2 bundles which related the invariant s_1 to the secant varieties of the curve inside certain extension spaces. For any n and r, we find a way to get information on the invariant s_r from the secant varieties of certain subvariety of a scroll over X. Using this geometric picture, we obtain a new proof of the Hirschowitz bound on s_r. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0905.1600 | |
| dc.identifier | http://arxiv.org/abs/0905.1600 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230317 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60, 14N05 | |
| dc.title | Secant varieties and Hirschowitz bound on vector bundles over a curve | |
| dc.type | text |