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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 semistablevector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smoothanticanonical 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 $\cal N$ themoduli space of all such pairs $(X',D')$, namely $D'$ is a smooth anticanonicaldivisor on a smooth moduli space of semistable vector bundles over the Riemannsurface $X'$. It turns out that the Kodaira-Spencer map from the tangent spaceto $\cal N$, at the point represented by the pair $(X,D)$, to $H^1(D, T_D)$ isan isomorphism. This is proved under the assumption that if $g =2$, then $n\neq2,3$, and if $g=3$, then $n\neq 2$.

Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve