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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Zusammenfassung: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.
ISSN:1815-0659