Article Dans Une Revue Compositio Mathematica Année : 2025

Vanishing Theorem for tame harmonic bundles via $L^2$-cohomology

Ya Deng
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Feng Hao
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Résumé

Using $L^2$ -methods, we prove a vanishing theorem for tame harmonic bundles over quasicompact Kähler manifolds in a very general setting. As a special case, we give a completely new proof of the Kodaira type vanishing theorems for Higgs bundles due to Arapura. To prove our vanishing theorem, we construct a fine resolution of the Dolbeault complex for tame harmonic bundles via the complex of sheaves of $L^2$ -forms, and we establish the Hörmander $L^2$-estimate and solve $\bar{\partial}+\theta)$-equations for Higgs bundles $(E,\theta)$.

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Dates et versions

hal-04728266 , version 1 (09-04-2025)

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Ya Deng, Feng Hao. Vanishing Theorem for tame harmonic bundles via $L^2$-cohomology. Compositio Mathematica, 2025, 160 (12), pp.2828-2855. ⟨10.1112/S0010437X24007504⟩. ⟨hal-04728266⟩
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