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arXiv · 1912.02586

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

Ya Deng·Feng Hao
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Abstract

Using $L^2$-methods, we prove a vanishing theorem for tame harmonic bundles over quasi-compact 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 $(\bar{\partial}_E+θ)$-equations for Higgs bundles $(E,θ)$.

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Ya Deng, Feng Hao. 2022-04-23. Vanishing theorem for tame harmonic bundles via $L^2$-cohomology. https://arxiv.org/abs/1912.02586

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