Vector bundles with a fixed determinant on an irreducible nodal curve
| dc.creator | Bhosle, Usha N | |
| dc.date | 2005-12-14 | |
| dc.date.accessioned | 2026-07-07T06:55:15Z | |
| dc.date.available | 2026-07-07T06:55:15Z | |
| dc.description | Let $M$ be the moduli space of generalized parabolic bundles (GPBs) of rank $r$ and degree $d$ on a smooth curve $X$. Let $M_{\bar L}$ be the closure of its subset consisting of GPBs with fixed determinant ${\bar L}$. We define a moduli functor for which $M_{\bar L}$ is the coarse moduli scheme. Using the correspondence between GPBs on $X$ and torsion-free sheaves on a nodal curve $Y$ of which $X$ is a desingularization, we show that $M_{\bar L}$ can be regarded as the compactified moduli scheme of vector bundles on $Y$ with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves on $Y$. The relation to Seshadri--Nagaraj conjecture is studied. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512318 | |
| dc.identifier | http://arxiv.org/abs/math/0512318 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 445-451 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106221 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60 | |
| dc.title | Vector bundles with a fixed determinant on an irreducible nodal curve | |
| dc.type | text |