19 citations · 68 across the 27 of their papers we have counts for
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Geometric monodromies, mixed Hodge numbers of motivic Milnor fibers and Newton polyhedra
Kiyoshi Takeuchi
We introduce the theory of local and global monodromies of polynomials in cohomology groups in various geometric situations, focusing on its relations with toric geometry and motiv…
Fourier transforms of irregular holonomic D-modules, singularities at infinity of meromorphic functions and irregular characteristic cycles
Kiyoshi Takeuchi
Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Four…
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…
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…
On Some Topological Properties of Fourier Transforms of Regular Holonomic D-Modules
Yohei Ito, Kiyoshi Takeuchi
We study Fourier transforms of regular holonomic D-modules. In particular we show that their solution complexes are monodromic. An application to direct images of some irregular ho…
On Irregularities of Fourier Transforms of Regular Holonomic D-Modules
Yohei Ito, Kiyoshi Takeuchi
We study Fourier transforms of regular holonomic D-modules. By using the theory of Fourier-Sato transforms of enhanced ind-sheaves developed by Kashiwara-Schapira and D'Agnolo-Kash…