Higgs bundles and indecomposable parabolic bundles over the projective line

2016/09/15 by Emmanuel Letellier, Letellier, Emmanuel · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1609.04875

openalex publication_date 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological interpretation for this counting using the moduli space of Higgs fields on the given vector bundle over the complex projective line with prescribed residues. We prove a certain number of results which bring evidences to the main conjecture. We detail the case of rank 2 vector bundles.

Citations

• Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)
• Spherical Hall algebras of a weighted projective curve

Cited by

• Twisted spectral correspondence and torus knots

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• Indecomposable vector bundles and stable Higgs bundles over smooth projective curves
• Two-dimensional moduli spaces of irregular Higgs bundles
• Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications
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• Counting Higgs bundles