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.

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)

References in corpus (3)

• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules
• E_1-degeneration of the irregular Hodge filtration (with an appendix by Morihiko Saito)
• A twistor approach to the Kontsevich complexes

Cited by in corpus (13)

• Hodge theory of Kloosterman connections
• Algebraic aspects of hypergeometric differential equations
• Hodge-Tate conditions for Landau-Ginzburg models
• Irregular Hodge filtration of some confluent hypergeometric systems
• Examples of hypergeometric twistor $\mathcal{D}$-modules
• A twistor approach to the Kontsevich complexes
• Hodge numbers of motives attached to Kloosterman and Airy moments
• Hodge properties of Airy moments
• Rescalability of integrable mixed twistor $D$-modules
• A description of monodromic mixed Hodge modules
• Irregular Hodge filtration of hypergeometric differential equations
• The Künneth Formula for the Twisted de Rham and Higgs Cohomologies
• Singularities of functions: a global point of view