Transformation Groups

, Volume 18, Issue 4, pp 995–1018 | Cite as

Polygons in Minkowski three space and parabolic Higgs bundles of rank 2 on \( \mathbb{C}{{\mathbb{P}}^1} \)

  • Indranil Biswas*Email author
  • Carlos Florentino**
  • Leonor Godinho***
  • Alessia Mandini****


Consider the moduli space of parabolic Higgs bundles (E, Φ) of rank two on ℂℙ1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with the natural involution defined by \( \left( {E,\varPhi } \right)\mapsto \left( {E,-\varPhi } \right) \). We study the fixed point locus of this involution. In [GM], this moduli space with involution was identified with the moduli space of hyperpolygons equipped with a certain natural involution. Here we identify the fixed point locus with the moduli spaces of polygons in Minkowski 3-space. This identification yields information on the connected components of the fixed point locus.


Modulus Space Vector Bundle Holomorphic Vector Bundle Coadjoint Orbit Circle Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Indranil Biswas*
    • 1
    Email author
  • Carlos Florentino**
    • 2
  • Leonor Godinho***
  • Alessia Mandini****
  1. 1.School of Mathematics Tata Institute of Fundamental ResearchBombayIndia
  2. 2.Departamento Matemática CAMGSD–LARSYS Instituto Superior TécnicoLisbonPortugal

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