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On $V$-filtration, Hodge filtration and Fourier transform
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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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Cited by 1 Pith paper
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Hodge microsheaves on cotangent bundles and plumbings
A new category of Hodge microsheaves is defined via gluing mixed Hodge modules, and it reproduces Hain's loop Hodge structure on P^n and gives a mixed-geometric proof of Etgü–Lekili Koszul duality.
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