Stratifications on the nilpotent cone of the moduli space of Hitchin pairs

Gothen, Peter B.; Zúñiga-Rojas, Ronald A.

doi:10.1007/s13163-021-00400-3

Cited by 2 publications

(1 citation statement)

References 16 publications

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“…Several authors have recently investigated more closely the structure of the structure of the nilpotent cone and the wobbly locus in general situations: Bozec [Boz22], Gothen-Zúñiga-Rojas [GnR22], Pal-Pauly [PP21], Peón-Nieto [PN20,FGOPN23], Zelaci [Zel20], Hellmann [Hel21], Hausel-Hitchin [HH22].…”

Section: The Case Of Genus 2 and Rankmentioning

confidence: 99%

Parabolic Hecke eigensheaves

DONAGI,

PANTEV

2022

ast

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Following the strategy outlined in [DP09, DP22] for bundles of rank 2 on a smooth projective curve of genus 2, we construct flat connections over the moduli of stable bundles, with singularities along the wobbly locus. We verify that the associated Dmodules are Hecke eigensheaves. The local systems are constructed by the nonabelian Hodge correspondence from Higgs bundles. The spectral varieties of the Higgs bundles are the Hitchin fibers corresponding to the Hecke eigenvalues.

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Section: The Case Of Genus 2 and Rankmentioning

confidence: 99%

Parabolic Hecke eigensheaves

DONAGI,

PANTEV

2022

ast

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Three instability stratifications of the stack of Higgs bundles on a smooth projective curve

Hamilton

2023

The Quarterly Journal of Mathematics

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We study three instability stratifications of the stack of twisted Higgs bundle of a fixed rank and degree on a smooth complex projective curve. The first is the Harder–Narasimhan (HN) stratification, defined by the instability type of the Higgs bundle. The second is the bundle Harder–Narasimhan (bHN) stratification, defined by the instability type of the underlying bundle. While an unstable HN stratum fibres over the stack parameterizing Higgs bundles which are isomorphic to their HN graded, this is not true for Higgs bundles of unstable bHN type. Obtaining such a fibration requires refining the bHN stratification; this is the third instability stratification. After introducing these three stratifications, we establish comparison results. In particular, we obtain explicit criteria for determining semistability of a Higgs bundle of low rank with unstable underlying bundle. Then we show how the HN and bHN stratifications can be used to filter the stack of Higgs bundles by global quotient stacks in two different ways. Finally, we use these filtrations to relate the HN and bHN stratifications to GIT instability stratifications and the refined bHN stratification to a Bialynicki–Birula stratification.

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Stratifications on the nilpotent cone of the moduli space of Hitchin pairs

Cited by 2 publications

References 16 publications

Parabolic Hecke eigensheaves

Parabolic Hecke eigensheaves

Three instability stratifications of the stack of Higgs bundles on a smooth projective curve

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