Matthieu Kochersperger

arXiv2018

Mixed Hodge modules without slope

In this article we are interested in morphisms without slope for mixed Hodge modules. We first show the commutativity of iterated nearby cycles and vanishing cycles applied to a mixed Hodge module in the case of a morphism without slope. Then we define the notion "strictly without slope" for a mixed Hodge module and we show the preservation of this condition under the direct image by a proper morphism. As an application we prove the compatibility of the Hodge filtration and Kashiwara-Malgrange filtrations for some pure Hodge modules with support an hypersurface with quasi-ordinary singularities.

math.AG↗

arXiv2016

Comparison theorem for nearby cycles of a morphism without slopes

The goal of this article is to prove the comparison theorem between algebraic and topological nearby cycles of a morphism without slopes. We prove in particular that for a family of holomorphic functions without slopes, if we iterate comparison isomorphisms for nearby cycles of each function the result is independent of the order of iteration.

math.AG↗