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Abstract
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We prove that a generically regular semisimple Higgs bundle equipped with a
nondegenerate symmetric pairing on any Riemann surface always has a harmonic metric
compatible with the pairing. We also study the classification of such compatible
harmonic metrics in the case where the Riemann surface is the complement of a finite
set
in
a compact Riemann surface. In particular, we prove the uniqueness of a compatible
harmonic metric if the Higgs bundle is wild and regular semisimple at each point of
.
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Keywords
harmonic bundle, nondegenerate symmetric product, real
structure
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Mathematical Subject Classification
Primary: 53C07
Secondary: 58E15, 14D21, 81T13
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Milestones
Received: 15 October 2022
Revised: 23 July 2023
Accepted: 9 August 2023
Published: 21 November 2023
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Publishers). |
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