Stratifications on the Moduli Space of Higgs Bundles

Abstract

The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the Harder-Narasimhan type of the vector bundle underlying a Higgs bundle. While these two stratification coincide in the case of rank two Higgs bundles, this is not the case in higher rank. In this paper we analyze the relation between the two stratifications for the moduli space of rank three Higgs bundles.

18 pages; v2: extended results to the non-coprime case, other minor corrections, updated references; v3, v4: corrected typos; to appear in Portugaliae Mathematica

References in corpus (1)

• Higgs bundles over elliptic curves for complex reductive Lie groups

Cited by in corpus (3)

• Non-Abelian Hodge Theory and Related Topics
• Simpson Filtration and Oper Stratum Conjecture
• Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs