Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactifying the rank two Hitchin system via spectral data on
  semistable curves   We study resolutions of the rational map to the moduli space of stable curves
that associates with a point in the Hitchin base the spectral curve. In the
rank two case the answer is given in terms of the space of quadratic
multi-scale differentials introduced in [BCGGM3]. This space defines a
compactification (of the projectivization) of the regular locus of the
$\mathrm{GL}(2,\mathbb{C})$-Hitchin base and provides a compactification of the
Hitchin system by compactified Jacobians of pointed stable curves. We show how
the classical $\mathrm{GL}(2,\mathbb{C})$- and
$\mathrm{SL}(2,\mathbb{C})$-spectral correspondence extend to the compactified
Hitchin system by a correspondence along an admissible cover between
torsion-free rank $1$ sheaves and (multi-scale) Higgs pairs of rank $2$.

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The categories of this paper are: atom-ph
19
The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys