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- W2949383409 abstract "Let $X$ be a compact connected Riemann surface of genus $g$, with $ggeq 2$, and ${cal M}_{xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $ngeq 2$, 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 $nneq 2,3$, and if $g=3$, then $nneq 2$." @default.
- W2949383409 created "2019-06-27" @default.
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- W2949383409 date "1999-04-08" @default.
- W2949383409 modified "2023-09-27" @default.
- W2949383409 title "Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve" @default.
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