Compactifying the rank two Hitchin system via spectral data on semistable curves
arxiv(2022)
摘要
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
GL(2,ℂ)-Hitchin base and provides a compactification of the
Hitchin system by compactified Jacobians of pointed stable curves. We show how
the classical GL(2,ℂ)- and
SL(2,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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关键词
hitchin system,spectral data,curves
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