Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreducible cone spherical metrics and stable extensions of two line
  bundles   A cone spherical metric is called irreducible if any developing map of the
metric does not have monodromy in ${\rm U(1)}$. By using the theory of
indigenous bundles, we construct on a compact Riemann surface $X$ of genus $g_X
\geq 1$ a canonical surjective map from the moduli space of stable extensions
of two line bundles to that of irreducible metrics with cone angles in $2 \pi
\mathbb{Z}_{>1}$, which is generically injective in the algebro-geometric sense
as $g_X \geq 2$. As an application, we prove the following two results about
irreducible metrics:
  $\bullet$ as $g_X \geq 2$ and $d$ is even and greater than $12g_X - 7$, the
effective divisors of degree $d$ which could be represented by irreducible
metrics form an arcwise connected Borel subset of Hausdorff dimension $\geq
2(d+3-3g_X)$ in ${\rm Sym}^d(X)$;
  $\bullet$ as $g_X \geq 1$, for almost every effective divisor $D$ of degree
odd and greater than $2g_X-2$ on $X$, there exist finitely many cone spherical
metrics representing $D$.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an