Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2012
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| _version_ | 1866913334514679808 |
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| author | Biswas, Indranil Florentino, Carlos Godinho, Leonor Mandini, Alessia |
| author_facet | Biswas, Indranil Florentino, Carlos Godinho, Leonor Mandini, Alessia |
| contents | Consider the moduli space of parabolic Higgs bundles (E,Φ) of rank two on CP^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 (E,Φ)\mapsto (E,-Φ). 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1206_1720 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1 Biswas, Indranil Florentino, Carlos Godinho, Leonor Mandini, Alessia Algebraic Geometry Differential Geometry Symplectic Geometry 14D20, 14H60, 53C26, 53D20 Consider the moduli space of parabolic Higgs bundles (E,Φ) of rank two on CP^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 (E,Φ)\mapsto (E,-Φ). 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. |
| title | Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1 |
| topic | Algebraic Geometry Differential Geometry Symplectic Geometry 14D20, 14H60, 53C26, 53D20 |
| url | https://arxiv.org/abs/1206.1720 |