Polygons in Minkowski three space and parabolic Higgs bundles of rank 2 on mathbb{C}{{mathbb{P}}^1} |
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Authors: | Indranil Biswas Carlos Florentino Leonor Godinho Alessia Mandini |
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Affiliation: | 1. School of Mathematics Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400005, India 2. Departamento Matemática CAMGSD–LARSYS Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal
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Abstract: | Consider the moduli space of parabolic Higgs bundles (E, Φ) of rank two on ??1 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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