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Real Higgs pairs and non-abelian Hodge correspondence on a Klein surface
dc.contributor.author | Biswas, Indranil | es-ES |
dc.contributor.author | Calvo Pascual, Luis Ángel | es-ES |
dc.contributor.author | García Prada, Óscar | es-ES |
dc.date.accessioned | 2024-02-23T10:21:13Z | |
dc.date.available | 2024-02-23T10:21:13Z | |
dc.date.issued | 2023-12-06 | es_ES |
dc.identifier.issn | 1019-8385 | es_ES |
dc.identifier.uri | https://dx.doi.org/10.4310/CAG.2023.v31.n2.a9 | es_ES |
dc.identifier.uri | http://hdl.handle.net/11531/86938 | |
dc.description | Artículos en revistas | es_ES |
dc.description.abstract | . | es-ES |
dc.description.abstract | We introduce real structures on L-twisted Higgs pairs over a compact connected Riemann surface X equipped with an antiholomorphic involution, where L is a holomorphic line bundle on X with a real structure, and prove a Hitchin–Kobayashi correspondence for the L-twisted Higgs pairs. Real GR-Higgs bundles, where GR is a real form of a connected semisimple complex affine algebraic group G, constitute a particular class of examples of these pairs. In this case, the real structure of the moduli space of G-Higgs pairs is defined using a conjugation of G that commutes with the one defining the real form GR and a compact conjugation of G preserving GR. We establish a homeomorphism between the moduli space of real GR-Higgs bundles and the moduli space of representations of the fundamental group of X in GR that can be extended to a representation of the orbifold fundamental group of X into a certain enlargement of GR with quotient Z/2Z. Finally, we show how real GR-Higgs bundles appear naturally as fixed points of certain anti-holomorphic involutions of the moduli space of GR-Higgs bundles, constructed using the real structures on G and X. A similar result is proved for the representations of the orbifold fundamental group. | en-GB |
dc.format.mimetype | application/pdf | es_ES |
dc.language.iso | en-GB | es_ES |
dc.rights | Creative Commons Reconocimiento-NoComercial-SinObraDerivada España | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | es_ES |
dc.source | Revista: Communications in Analysis and Geometry, Periodo: 1, Volumen: 31, Número: 2, Página inicial: 485, Página final: 546 | es_ES |
dc.title | Real Higgs pairs and non-abelian Hodge correspondence on a Klein surface | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.description.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.rights.holder | es_ES | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |
dc.keywords | . | es-ES |
dc.keywords | Structures Higgs pairs Real GR-Higgs bundles Moduli space Orbifold fundamental group | en-GB |
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