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arXiv · 1609.04875

Higgs bundles and indecomposable parabolic bundles over the projective line

Emmanuel Letellier
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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.

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Emmanuel Letellier. 2016-09-15. Higgs bundles and indecomposable parabolic bundles over the projective line. https://arxiv.org/abs/1609.04875

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