On V-filtration, Hodge filtration and Fourier transform

Qianyu Chen ^[1] ; Bradley Dirks ^[1]
1. [1] University of Michigan–Ann Arbor
  
  University of Michigan–Ann Arbor
  
  City of Ann Arbor, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
Idioma: inglés
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Resumen
- For i : Z → X a closed immersion of smooth varieties, we study how the V-filtration along Z and the Hodge filtration on a mixed Hodge moduleMon 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.