Zobrazeno 1 - 10
of 349
pro vyhledávání: '"Takeuchi, Kiyoshi"'
Autor:
Kudomi, Kazuki, Takeuchi, Kiyoshi
Based on the recent progress in the irregular Riemann-Hilbert correspondence, we study the monodromies at infinity of the holomorphic solutions of Fourier transforms of holonomic D-modules in some situations. Formulas for their eigenvalues are obtain
Externí odkaz:
http://arxiv.org/abs/2409.00423
Autor:
Kudomi, Kazuki, Takeuchi, Kiyoshi
We study Fourier transforms of holonomic D-modules on the affine line and show that their enhanced solution complexes are described by a twisted Morse theory. We thus recover and even strengthen the well-known formula for their exponential factors i.
Externí odkaz:
http://arxiv.org/abs/2311.17395
Autor:
Takeuchi, Kiyoshi
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 motivic Milnor fibers, and moreover in the modern languages of nearby and v
Externí odkaz:
http://arxiv.org/abs/2308.09418
Autor:
Takeuchi, Kiyoshi
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 Fourier transforms of some irregular holonomic D-modules. For this purpose
Externí odkaz:
http://arxiv.org/abs/2211.04113
Autor:
Takeuchi, Kiyoshi
We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the monodromy conj
Externí odkaz:
http://arxiv.org/abs/2110.15780
The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, N\'emethi and Zaharia described them in terms of Newton polytopes. In this paper, we will show analogous results for rat
Externí odkaz:
http://arxiv.org/abs/2003.13308
Autor:
Nguyen, Tat Thang, Takeuchi, Kiyoshi
We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinatorial descriptions of their reduced Hodge spectra and Jordan normal fo
Externí odkaz:
http://arxiv.org/abs/1909.01809
Autor:
Ito, Yohei, Takeuchi, Kiyoshi
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 holonomic D-modules will be given. Moreover we give a new proof to the c
Externí odkaz:
http://arxiv.org/abs/1807.09147
Autor:
Ito, Yohei, Takeuchi, Kiyoshi
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-Kashiwara, a formula for their enhanced solution complexes will be obtaine
Externí odkaz:
http://arxiv.org/abs/1801.07444
Autor:
Saito, Takahiro, Takeuchi, Kiyoshi
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 express their motivic nearby fibers in terms of the geometric data of some N
Externí odkaz:
http://arxiv.org/abs/1603.00702