Stratifications on the moduli space of Higgs bundles

2015/11/30 by Peter B. Gothen, Ronald A. Zúñiga-Rojas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics #Geometry #Higgs boson #Homotopy and Cohomology in Algebraic Topology #Mathematics #Moduli space #Particle physics #Physics #Pure mathematics #Topology (electrical circuits) #math.AG #msc:14D07 #msc:14H60

paper · pdf · doi:10.4171/pm/1996

published as Portugaliae Mathematica 74 (2017), 127-148 · 18 pages; v2: extended results to the non-coprime case, other minor corrections, updated references; v3, v4: corrected typos; to appear in Portugaliae Mathematica

arxiv created 2016/11/03 · openalex publication_date 2017/11/10 · arxiv updated 2018/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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