Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector bundles and connections on Riemann surfaces with projective
  structure   Let ${\mathcal B}_g(r)$ be the moduli space of triples of the form $(X,\,
K^{1/2}_X,\, F)$, where $X$ is a compact connected Riemann surface of genus
$g$, with $g\, \geq\, 2$, $K^{1/2}_X$ is a theta characteristic on $X$, and $F$
is a stable vector bundle on $X$ of rank $r$ and degree zero. We construct a
$T^*{\mathcal B}_g(r)$--torsor ${\mathcal H}_g(r)$ over ${\mathcal B}_g(r)$.
This generalizes on the one hand the torsor over the moduli space of stable
vector bundles of rank $r$, on a fixed Riemann surface $Y$, given by the moduli
space of holomorphic connections on the stable vector bundles of rank $r$ on
$Y$, and on the other hand the torsor over the moduli space of Riemann surfaces
given by the moduli space of Riemann surfaces with a projective structure. It
is shown that ${\mathcal H}_g(r)$ has a holomorphic symplectic structure
compatible with the $T^*{\mathcal B}_g(r)$--torsor structure. We also describe
${\mathcal H}_g(r)$ in terms of the second order matrix valued differential
operators. It is shown that ${\mathcal H}_g(r)$ is identified with the
$T^*{\mathcal B}_g(r)$--torsor given by the sheaf of holomorphic connections on
the theta line bundle over ${\mathcal B}_g(r)$.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph