Takahiro Saito

activity

20162022

collaborators

7 papers

math.AG2022

The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration

Takahiro Saito

For an algebraic vector bundle $E$ over a smooth algebraic variety $X$ , a monodromic $D$ -module on $E$ is decomposed into a direct sum of some $O$ -modules on $X$ . We show that the…

math.AG2020

A description of monodromic mixed Hodge modules

Takahiro Saito

For a smooth algebraic variety $X$ , a monodromic $D$ -module on $X \times C$ is decomposed into a direct sum of some $D$ -modules on $X$ . We show that the Hodge filtration of…

math.AG2020

The bifurcation set of a rational function via Newton polytopes

Tat Thang Nguyen, Takahiro Saito, Kiyoshi Takeuchi

The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, Némethi and Zaharia described them in terms of New…

math.AG2019

Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

Tat Thang Nguyen, Kiyoshi Takeuchi

We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinat…

math.AG2017

Milnor monodromies and mixed Hodge structures for non-isolated hypersurface singularities

Takahiro Saito

We study the Milnor monodromies of non-isolated hypersurface singularities and show that the reduced cohomology groups of the Milnor fibers are concentrated in the middle degree fo…

math.AG2016

On the monodromies and the limit mixed Hodge structures of families of algebraic varieties

Takahiro Saito, Kiyoshi Takeuchi

We study the monodromies and the limit mixed Hodge structures of families of complete intersection varieties over a punctured disk in the complex plane. For this purpose, we expres…