On the Brill-Noether theory for K3 surfaces
| dc.creator | Leyenson, Maxim | |
| dc.date | 2005-11-27 | |
| dc.date.accessioned | 2026-07-07T06:51:47Z | |
| dc.date.available | 2026-07-07T06:51:47Z | |
| dc.description | Let (S,H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c_1(E),H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of sheaves of different ranks on S, we prove our main theorem: polarized K3 surface which is generic in sense of moduli is also generic in sense of Brill-Noether theory (here H is the positive generator of the Picard group of S). In case of algebraic curves such a theorem, proved by Griffiths and Harris and, independently, by Lazarsfeld, is sometimes called ``the strong theorem of the Brill-Noether theory''. We finish by considering a number of projective examples. In particular, we construct explicitly Brill-Noether special K3 surfaces of genus 5 and 6 and show the relation with the theory of Brill-Noether special curves. | |
| dc.description | 38 pages; xypic is used; 8 PostScript pictures | |
| dc.identifier | https://arxiv.org/abs/math/0511659 | |
| dc.identifier | http://arxiv.org/abs/math/0511659 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105102 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J10;14J28;14J60 | |
| dc.title | On the Brill-Noether theory for K3 surfaces | |
| dc.type | text |