Abstract
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.
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*Supported by J. C. Bose Fellowship.
**Partially supported by FCT project PTDC/MAT/099275/2008.
***Partially supported by FCT projects PTDC/MAT/108921/2008 and PTDC/MAT/120411/2010.
****Supported by FCT grant SFRH/BPD/44041/2008 and FCT project PTDC/MAT/120411/2010.
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Biswas*, I., Florentino**, C., Godinho***, L. et al. Polygons in Minkowski three space and parabolic Higgs bundles of rank 2 on \( \mathbb{C}{{\mathbb{P}}^1} \) . Transformation Groups 18, 995–1018 (2013). https://doi.org/10.1007/s00031-013-9238-5
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DOI: https://doi.org/10.1007/s00031-013-9238-5