Portugaliae Mathematica
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Published online: 2017-11-10
Stratifications on the moduli space of Higgs bundles
Peter B. Gothen[1] and Ronald A. Zúñiga-Rojas[2] (1) Universidade do Porto, Portugal(2) 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.
Keywords: Moduli of Higgs bundles, Harder–Narasimhan filtrations, Hodge bundles, vector bundles
Gothen Peter, Zúñiga-Rojas Ronald: Stratifications on the moduli space of Higgs bundles. Port. Math. 74 (2017), 127-148. doi: 10.4171/PM/1996