On the irregular Hodge filtration of exponentially twisted mixed Hodge modules
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.
Keywords
Cite
@article{arxiv.1406.1339,
title = {On the irregular Hodge filtration of exponentially twisted mixed Hodge modules},
author = {Claude Sabbah and Jeng-Daw Yu},
journal= {arXiv preprint arXiv:1406.1339},
year = {2020}
}
Comments
53 pages. V2: 56 pages, Introduction partly rewritten. Final revised version to appear in Forum of Mathematics Sigma. V3: post-publication, small changes in the proof of (5.3) (thanks to Takahiro Saito for noticing a mistake)