On Lange's Conjecture
| dc.creator | Teixidor-i-Bigas, Montserrat | |
| dc.date | 1997-05-22 | |
| dc.date.accessioned | 2026-07-07T09:07:18Z | |
| dc.date.available | 2026-07-07T09:07:18Z | |
| dc.description | Let C be an algebraic curve of genus g. Let E be a vector bundle of rank n and degree d. Consider among all subbundles F' of E of rank n' those of maximal degree d'. Then s_n'(E)= n'd-nd'\le n'(n-n')g. If E is stable s_n'(E)>0 while if E is generic s_n'(E)\ge n'(n-n')(g-1) . The following statement was conjectured by Lange: If 0<s\le n'(n-n')(g-1), then there exist stable vector bundles with s_n'(E)=s. We prove this result for the generic curve. We also clarify what happens in the interval n'(n-n')(g-1)<s\le n'(n-n')g Our method uses a degeneration argument to a reducible curve. A similar result has been obtained by L.Bambrila-Paz and H.Lange using a different method. | |
| dc.description | plain tex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9705019 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9705019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150324 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On Lange's Conjecture | |
| dc.type | text |