Higgs bundles twisted by a vector bundle

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also s...

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Detalles Bibliográficos
Autores: Gallego, G., García-Prada, O., Narasimhan, M.S.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2024
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/381371
Acceso en línea:http://hdl.handle.net/10261/381371
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189897187&doi=10.1142%2fS0129167X24410076&partnerID=40&md5=671b8bd792968e5051e555b356f4f4f7
Access Level:acceso abierto
Palabra clave:Higgs bundles
Hitchin map
Hitchin-Kobayashi correspondence
Spectral correspondence
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spelling Higgs bundles twisted by a vector bundleGallego, G.García-Prada, O.Narasimhan, M.S.Higgs bundlesHitchin mapHitchin-Kobayashi correspondenceSpectral correspondenceIn this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin-Kobayashi correspondence for a generalization of Hitchin's equations to this situation. In a certain sense, this theory lies halfway between the theories of Higgs bundles on a curve and on a higher-dimensional variety. © 2024 World Scientific Publishing Company.The first and second authors thank the Indian Institute of Science (Bangalore) and the International Centre for Theoretical Sciences (Bangalore) for hospitality during the visits that led to this collaboration, and during the programme Moduli of bundles and related structures (Code: ICTS/mbrs2020/02). We thank Nigel Hitchin and Tony Pantev for fruitful discussions. We also thank David Alfaya, Peter Dalakov, Andr´e Oliveira, and the anonymous referee for their useful comments.Peer reviewedWorld Scientific PublishingConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/381371https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189897187&doi=10.1142%2fS0129167X24410076&partnerID=40&md5=671b8bd792968e5051e555b356f4f4f7reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)InglésInternational Journal of Mathematicshttps://doi.org/10.1142/S0129167X24410076Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3813712026-05-22T06:33:51Z
dc.title.none.fl_str_mv Higgs bundles twisted by a vector bundle
title Higgs bundles twisted by a vector bundle
spellingShingle Higgs bundles twisted by a vector bundle
Gallego, G.
Higgs bundles
Hitchin map
Hitchin-Kobayashi correspondence
Spectral correspondence
title_short Higgs bundles twisted by a vector bundle
title_full Higgs bundles twisted by a vector bundle
title_fullStr Higgs bundles twisted by a vector bundle
title_full_unstemmed Higgs bundles twisted by a vector bundle
title_sort Higgs bundles twisted by a vector bundle
dc.creator.none.fl_str_mv Gallego, G.
García-Prada, O.
Narasimhan, M.S.
author Gallego, G.
author_facet Gallego, G.
García-Prada, O.
Narasimhan, M.S.
author_role author
author2 García-Prada, O.
Narasimhan, M.S.
author2_role author
author
dc.contributor.none.fl_str_mv Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Higgs bundles
Hitchin map
Hitchin-Kobayashi correspondence
Spectral correspondence
topic Higgs bundles
Hitchin map
Hitchin-Kobayashi correspondence
Spectral correspondence
description In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin-Kobayashi correspondence for a generalization of Hitchin's equations to this situation. In a certain sense, this theory lies halfway between the theories of Higgs bundles on a curve and on a higher-dimensional variety. © 2024 World Scientific Publishing Company.
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/381371
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189897187&doi=10.1142%2fS0129167X24410076&partnerID=40&md5=671b8bd792968e5051e555b356f4f4f7
url http://hdl.handle.net/10261/381371
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189897187&doi=10.1142%2fS0129167X24410076&partnerID=40&md5=671b8bd792968e5051e555b356f4f4f7
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv International Journal of Mathematics
https://doi.org/10.1142/S0129167X24410076
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv World Scientific Publishing
publisher.none.fl_str_mv World Scientific Publishing
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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