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Infinitesimal deformations of a CalabiYau hypersurface of the moduli space of stable vector bundles over a curve  Indranil Biswas
; Leticia BrambilaPaz
;  Date: 
8 Apr 1999  Subject:  Algebraic Geometry  math.AG  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 CalabiYau variety. We compute the number of moduli of $D$, namely $dim H^1(D, T_D)$, to be $3g4 + dim H^0({cal M}_{xi}, K^{1}_{{cal M}_{xi}})$. 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 KodairaSpencer 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 $n
eq 2,3$, and if $g=3$, then $n
eq 2$.  Source:  arXiv, math.AG/9904033  Services:  Forum  Review  PDF  Favorites 


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