On the irregular Hodge filtration of exponentially twisted mixed Hodge modules

TL;DR

This paper develops the irregular Hodge filtration for exponentially twisted mixed Hodge modules, demonstrating its properties and applications, including the Laplace transform of Gauss-Manin systems and connections to Kontsevich bundles.

Contribution

It extends the construction of the irregular Hodge filtration to a broader setting and proves strictness of push-forward filtered D-modules using Mochizuki's theory.

Findings

Strictness of push-forward filtered D-modules established

Expression of irregular Hodge filtration via Harder-Narasimhan filtration

Application to Laplace transforms of Gauss-Manin systems

Abstract

Given a mixed Hodge module and a meromorphic function f on a complex manifold, we associate to these data a filtration (the irregular Hodge filtration) on the exponentially twisted holonomic module, which extends the construction of arXiv:1302.4537. We show the strictness of the push-forward filtered D-module through any projective morphism, by using the theory of mixed twistor D-modules of T. Mochizuki. We consider the example of the rescaling of a regular function f, which leads to an expression of the irregular Hodge filtration of the Laplace transform of the Gauss-Manin systems of f in terms of the Harder-Narasimhan filtration of the Kontsevich bundles associated with f.