$L^2$-complexes and twistor complexes of tame harmonic bundles

Takuro Mochizuki

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arXiv · 2204.10443

$L^2$-complexes and twistor complexes of tame harmonic bundles

Takuro Mochizuki

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Abstract

Let $f:X\to Y$ be a morphism of complex manifolds. Suppose that $X$ is a K\"ahler manifold. Let $(\mathcal{T},\mathcal{S})$ be a regular polarized pure twistor $\mathcal{D}$-module of weight $w$ on $X$ whose support is proper over $Y$. We prove the Hard Lefschetz Theorem for the push-forward of $(\mathcal{T},\mathcal{S})$ by $f$. As one of the key steps, we obtain the twistor version of a theorem of Kashiwara and Kawai about the Hodge structure on the intersection complex of polarized variation of Hodge structure.

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Takuro Mochizuki. 2022-04-22. $L^2$-complexes and twistor complexes of tame harmonic bundles. https://arxiv.org/abs/2204.10443

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