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arXiv · 1406.1339

On the irregular Hodge filtration of exponentially twisted mixed Hodge modules

Claude Sabbah·Jeng-Daw Yu
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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.

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Claude Sabbah, Jeng-Daw Yu. 2014-06-05. On the irregular Hodge filtration of exponentially twisted mixed Hodge modules. https://doi.org/10.1017/fms.2015.8

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