Unramified covers and branes on the Hitchin system

Detalhes bibliográficos
Autor(a) principal: André Oliveira
Data de Publicação: 2021
Outros Autores: Gothen, PB, Emilio Franco, Ana Peon-Nieto
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/10216/130402
Resumo: We study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then 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 singular locus of the Hitchin fibration. As a particular case, our construction describes the behavior under mirror symmetry of the fixed loci for the action of tensorization by a line bundle of order n. These loci play a key role in the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces. (C) 2020 Published by Elsevier Inc.
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spelling Unramified covers and branes on the Hitchin systemWe study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then 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 singular locus of the Hitchin fibration. As a particular case, our construction describes the behavior under mirror symmetry of the fixed loci for the action of tensorization by a line bundle of order n. These loci play a key role in the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces. (C) 2020 Published by Elsevier Inc.20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/130402eng0001-870810.1016/j.aim.2020.107493André OliveiraGothen, PBEmilio FrancoAna Peon-Nietoinfo: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:RCAAP2023-11-29T14:37:34Zoai:repositorio-aberto.up.pt:10216/130402Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:05:27.321578Repositório 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
André Oliveira
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 André Oliveira
author_facet André Oliveira
Gothen, PB
Emilio Franco
Ana Peon-Nieto
author_role author
author2 Gothen, PB
Emilio Franco
Ana Peon-Nieto
author2_role author
author
author
dc.contributor.author.fl_str_mv André Oliveira
Gothen, PB
Emilio Franco
Ana Peon-Nieto
description We study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then 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 singular locus of the Hitchin fibration. As a particular case, our construction describes the behavior under mirror symmetry of the fixed loci for the action of tensorization by a line bundle of order n. These loci play a key role in the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces. (C) 2020 Published by Elsevier Inc.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
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dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/10216/130402
url https://hdl.handle.net/10216/130402
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0001-8708
10.1016/j.aim.2020.107493
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