English

Higgs bundles and indecomposable parabolic bundles over the projective line

Algebraic Geometry 2016-09-19 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.1609.04875,
  title  = {Higgs bundles and indecomposable parabolic bundles over the projective line},
  author = {Emmanuel Letellier},
  journal= {arXiv preprint arXiv:1609.04875},
  year   = {2016}
}