Abstract
For \(i:Z\hookrightarrow X\) a closed immersion of smooth varieties, we study how the V-filtration along Z and the Hodge filtration on a mixed Hodge module \({\mathcal {M}}\) 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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Acknowledgements
The authors are extremely grateful to their respective advisers, Christian Schnell and Mircea Mustaţă. Without them this project would not have been possible. We would also like to thank Mihnea Popa for several suggestions and questions. QC thanks Guodu Chen and Mads Villadsen for reading a draft of this paper. BD is thankful to Sebastián Olano, James Hotchkiss and Jack Carlisle for many useful conversations. We would like to thank the anonymous referee for various suggestions and corrections.
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Bradley Dirks was partially supported by NSF Grant DMS-1840234.
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