Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A desingularization of the moduli space of rank 2 Higgs bundles over a
  curve   Let $X$ be a smooth complex projective curve of genus $g\geq 3$. Let
$\mathbf{M}_2$ be the moduli space of semistable rank $2$ Higgs bundles with
trivial determinant over $X$. We construct a desingularization $\mathbf{S}$ of
$\mathbf{M}_2$ as a closed subvariety of a moduli space. We prove that
$\mathbf{S}$ is a nonsingular variety containing the stable locus of
$\mathbf{M}_2$ as an open dense subvariety. On the other hand, there is another
desingularization $\mathbf{K}$ of $\mathbf{M}_2$ obtained from Kirwan's
algorithm. We show that $\mathbf{S}$ can be obtained after two blow-downs of
$\mathbf{K}$.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
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The categories of this paper are: physics
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con