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

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 $i^{\ast }$, $i^{!}$ 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.

52 pages. Comments are welcome. v4 comments: Minor changes, final version, to appear in Selecta Mathematica

References in corpus (1)

• An overview of Morihiko Saito's theory of mixed Hodge modules