Unramified covers and branes on the Hitchin system

Detalhes bibliográficos
Autor(a) principal: Franco, Emilio
Data de Publicação: 2020
Outros Autores: Gothen, Peter, Oliveira, Andre Gama, Peon-Nieto, Ana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10348/10309
Resumo: We study the locus of the moduli space of GL(n,C)-Higgs bundles on a curve givenby those Higgs bundles obtained by pushforward under a connected unramified cover. We equipthese loci with a hyperholomorphic bundle so that they can beviewed as BBB-branes, and weintroduce corresponding BAA-branes which can be describedvia Hecke modifications. Wethen show how these branes are naturally dual via explicit Fourier–Mukai transform (recall that GL(n,C) is Langlands self dual). It is noteworthy that these branes lie over the singularlocus of the Hitchin fibration.As a particular case, our construction describes the behavior under mirror symmetry of thefixed loci for the action of tensorization by a line bundle of ordern. These loci play a key rolein the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces.
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spelling Unramified covers and branes on the Hitchin systemHiggs bundlesMathematicsMirror SymmetryMathematicsWe study the locus of the moduli space of GL(n,C)-Higgs bundles on a curve givenby those Higgs bundles obtained by pushforward under a connected unramified cover. We equipthese loci with a hyperholomorphic bundle so that they can beviewed as BBB-branes, and weintroduce corresponding BAA-branes which can be describedvia Hecke modifications. Wethen show how these branes are naturally dual via explicit Fourier–Mukai transform (recall that GL(n,C) is Langlands self dual). It is noteworthy that these branes lie over the singularlocus of the Hitchin fibration.As a particular case, our construction describes the behavior under mirror symmetry of thefixed loci for the action of tensorization by a line bundle of ordern. These loci play a key rolein the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces.2020-12-03T10:32:04Z2020-11-01T00:00:00Z2020-11info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10348/10309engFranco, EmilioGothen, PeterOliveira, Andre GamaPeon-Nieto, Anainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-02T12:43:58Zoai:repositorio.utad.pt:10348/10309Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:03:36.258083Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Unramified covers and branes on the Hitchin system
title Unramified covers and branes on the Hitchin system
spellingShingle Unramified covers and branes on the Hitchin system
Franco, Emilio
Higgs bundles
Mathematics
Mirror Symmetry
Mathematics
title_short Unramified covers and branes on the Hitchin system
title_full Unramified covers and branes on the Hitchin system
title_fullStr Unramified covers and branes on the Hitchin system
title_full_unstemmed Unramified covers and branes on the Hitchin system
title_sort Unramified covers and branes on the Hitchin system
author Franco, Emilio
author_facet Franco, Emilio
Gothen, Peter
Oliveira, Andre Gama
Peon-Nieto, Ana
author_role author
author2 Gothen, Peter
Oliveira, Andre Gama
Peon-Nieto, Ana
author2_role author
author
author
dc.contributor.author.fl_str_mv Franco, Emilio
Gothen, Peter
Oliveira, Andre Gama
Peon-Nieto, Ana
dc.subject.por.fl_str_mv Higgs bundles
Mathematics
Mirror Symmetry
Mathematics
topic Higgs bundles
Mathematics
Mirror Symmetry
Mathematics
description We study the locus of the moduli space of GL(n,C)-Higgs bundles on a curve givenby those Higgs bundles obtained by pushforward under a connected unramified cover. We equipthese loci with a hyperholomorphic bundle so that they can beviewed as BBB-branes, and weintroduce corresponding BAA-branes which can be describedvia Hecke modifications. Wethen show how these branes are naturally dual via explicit Fourier–Mukai transform (recall that GL(n,C) is Langlands self dual). It is noteworthy that these branes lie over the singularlocus of the Hitchin fibration.As a particular case, our construction describes the behavior under mirror symmetry of thefixed loci for the action of tensorization by a line bundle of ordern. These loci play a key rolein the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-03T10:32:04Z
2020-11-01T00:00:00Z
2020-11
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10348/10309
url http://hdl.handle.net/10348/10309
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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