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ON THE IRREGULAR HODGE FILTRATION OF EXPONENTIALLY TWISTED MIXED HODGE MODULES

Part of: (Co)homology theory Singularities

Published online by Cambridge University Press:  25 May 2015

CLAUDE SABBAH  and
JENG-DAW YU
CLAUDE SABBAH
Affiliation:
UMR 7640 du CNRS, Centre de Mathématiques Laurent Schwartz, École polytechnique, F-91128 Palaiseau cedex, France; Claude.Sabbah@polytechnique.edu
JENG-DAW YU
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan; jdyu@ntu.edu.tw

Abstract

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Given a mixed Hodge module $\mathcal{N}$ 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 $\mathcal{N}\otimes \mathcal{E}^{f}$, which extends the construction of Esnault et al. ($E_{1}$-degeneration of the irregular Hodge filtration (with an appendix by Saito), J. reine angew. Math. (2015), doi:10.1515/crelle-2014-0118). We show the strictness of the push-forward filtered ${\mathcal{D}}$-module through any projective morphism ${\it\pi}:X\rightarrow Y$, by using the theory of mixed twistor ${\mathcal{D}}$-modules of 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 $f$.

MSC classification

Primary: 14F40: de Rham cohomology 32S35: Mixed Hodge theory of singular varieties 32S40: Monodromy; relations with differential equations and $D$-modules
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 3 , 2015 , e9
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2015

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