Vector bundles, dualities, and classical geometry on a curve of genus two
| dc.creator | Nguyen, Quang Minh | |
| dc.date | 2007-02-24 | |
| dc.date.accessioned | 2026-07-07T08:22:42Z | |
| dc.date.available | 2026-07-07T08:22:42Z | |
| dc.description | Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a canonical theta divisor $Θ$. The space $SU_C(3)$ is a double cover of $P^8=|3Θ|$ branched along a sextic hypersurface, the Coble sextic. In the dual $\check{P}^8=|3Θ|^*$, where $J^1$ is embedded, there is a unique cubic hypersurface singular along $J^1$, the Coble cubic. We prove that these two hypersurfaces are dual, inducing a non-abelian Torelli result. Moreover, by looking at some special linear sections of these hypersurfaces, we can observe and reinterpret some classical results of algebraic geometry in a context of vector bundles: the duality of the Segre-Igusa quartic with the Segre cubic, the symmetric configuration of 15 lines and 15 points, the Weddle quartic surface and the Kummer surface. | |
| dc.description | 21 pages. Supersedes math.AG/0408318. To appear in Internat. J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0702724 | |
| dc.identifier | http://arxiv.org/abs/math/0702724 | |
| dc.identifier | Internat. J. Math., Vol. 18 (2007), No. 5, 535--558 | |
| dc.identifier | doi:10.1142/S0129167X07004230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135738 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60; 14J70, 14E20, 14E30, 14C34 | |
| dc.title | Vector bundles, dualities, and classical geometry on a curve of genus two | |
| dc.type | text |