Stratifications on the moduli space of Higgs bundles

  • Peter Gothen

    Universidade do Porto, Portugal
  • Ronald A. Zúñiga-Rojas

    Universidad de Costa Rica, San José, Costa Rica


The moduli space of Higgs bundles has two stratifications. The Białynicki–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 stratifications 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.

Cite this article

Peter Gothen, Ronald A. Zúñiga-Rojas, Stratifications on the moduli space of Higgs bundles. Port. Math. 74 (2017), no. 2, pp. 127–148

DOI 10.4171/PM/1996