Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section

Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2024
1. Verfasser: Fujioka, Hitoshi
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212781
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Fujioka, Hitoshi
author_facet Fujioka, Hitoshi
citation_txt Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-sheeted branched covering of the Riemann surface. In particular, we give a condition for Higgs bundles in the Hitchin section on ℂ or ℂ* to have compatible harmonic metrics.
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spelling Fujioka, Hitoshi
2026-02-11T10:37:43Z
2024
Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages
1815-0659
2020 Mathematics Subject Classification: 53C07; 14D21
arXiv:2403.07258
https://nasplib.isofts.kiev.ua/handle/123456789/212781
https://doi.org/10.3842/SIGMA.2024.111
Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-sheeted branched covering of the Riemann surface. In particular, we give a condition for Higgs bundles in the Hitchin section on ℂ or ℂ* to have compatible harmonic metrics.
The author is grateful to the referees for their careful reading and valuable comments. The author is grateful to his supervisor, Takuro Mochizuki, for many discussions and helpful advice. The author thanks Qiongling Li and Takashi Ono for their helpful advice. This work was supported by JST SPRING, Grant Number JPMJSP2110.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
Article
published earlier
spellingShingle Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
Fujioka, Hitoshi
title Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
title_full Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
title_fullStr Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
title_full_unstemmed Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
title_short Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section
title_sort harmonic metrics for higgs bundles of rank 3 in the hitchin section
url https://nasplib.isofts.kiev.ua/handle/123456789/212781
work_keys_str_mv AT fujiokahitoshi harmonicmetricsforhiggsbundlesofrank3inthehitchinsection