For logarithmic G-Higgs bundles with nilpotent residues, B(Φ,Φ) defines a logarithmic quadratic one-form on pointed Teichmüller space and equals the variation of energy for tame nilpotent harmonic bundles under positive decay near punctures.
Geometry of moduli spaces of Higgs bundles
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abstract
We construct a Petersson-Weil type K\"ahler form on the moduli spaces of Higgs bundles over a compact K\"ahler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Petersson-Weil K\"ahler form is computed. We also show that, under certain assumptions, a moduli space of Higgs bundles supports of natural hyper-K\"ahler structure.
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math.DG 1years
2026 1verdicts
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Quadratic one-forms on logarithmic Higgs moduli
For logarithmic G-Higgs bundles with nilpotent residues, B(Φ,Φ) defines a logarithmic quadratic one-form on pointed Teichmüller space and equals the variation of energy for tame nilpotent harmonic bundles under positive decay near punctures.