Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli
  space of stable vector bundles over a curve   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 $n\neq 2$.

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The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph