Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve
| dc.creator | Biswas, Indranil | |
| dc.creator | Brambila-Paz, Leticia | |
| dc.date | 1999-04-08 | |
| dc.date.accessioned | 2026-07-07T05:28:37Z | |
| dc.date.available | 2026-07-07T05:28:37Z | |
| dc.description | Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_ξ$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical divisor $D$ on ${\cal M}_ξ$. So $D$ is a Calabi-Yau variety. We compute the number of moduli of $D$, namely $\dim H^1(D, T_D)$, to be $3g-4 + \dim H^0({\cal M}_ξ, K^{-1}_{{\cal M}_ξ})$. Denote by $\cal N$ the moduli space of all such pairs $(X',D')$, namely $D'$ is a smooth anticanonical divisor on a smooth moduli space of semistable vector bundles over the Riemann surface $X'$. It turns out that the Kodaira-Spencer map from the tangent space to $\cal N$, at the point represented by the pair $(X,D)$, to $H^1(D, T_D)$ is an isomorphism. This is proved under the assumption that if $g =2$, then $n\neq 2,3$, and if $g=3$, then $n\neq 2$. | |
| dc.description | AMS-LaTex file | |
| dc.identifier | https://arxiv.org/abs/math/9904033 | |
| dc.identifier | http://arxiv.org/abs/math/9904033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78332 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve | |
| dc.type | text |