Mathematics – Algebraic Geometry
Scientific paper
1999-04-08
Mathematics
Algebraic Geometry
AMS-LaTex file
Scientific paper
Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ 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 ${\cal M}_{\xi}$. So $D$ is a Calabi-Yau variety. We compute the number of moduli of $D$, namely $\dim H^1(D, T_D)$, to be $3g-4 + \dim H^0({\cal M}_{\xi}, K^{-1}_{{\cal M}_{\xi}})$. 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 $n\neq 2$.
Biswas Indranil
Brambila-Paz Leticia
No associations
LandOfFree
Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-398565