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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Fujioka, Hitoshi
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212781
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Harmonic Metrics for Higgs Bundles of Rank 3 in the Hitchin Section. Hitoshi Fujioka. SIGMA 20 (2024), 111, 21 pages

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-...