On $V$-filtration, Hodge filtration and Fourier transform

Qianyu Chen; Bradley Dirks

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arXiv · 2111.04622

On $V$-filtration, Hodge filtration and Fourier transform

Qianyu Chen·Bradley Dirks

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Abstract

For $i : Z \to X$ a closed immersion of smooth varieties, we study how the $V$-filtration along $Z$ and the Hodge filtration on a mixed Hodge module $M$ on $X$ interact with each other. We also give a formula for the functors $i^*$, $i^!$ in terms of this $V$-filtration. As applications, we obtain results on the Hodge filtration of monodromic mixed Hodge modules and we give a Hodge theoretic proof of Skoda's theorem on multiplier ideals. Finally, we use the results to study the Fourier-Laplace transform of a monodromic mixed Hodge module.

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Qianyu Chen, Bradley Dirks. 2021-11-08. On $V$-filtration, Hodge filtration and Fourier transform. https://arxiv.org/abs/2111.04622

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