On Irregularities of Fourier Transforms of Regular Holonomic D-Modules

2018/01/23 by Yôhei Itô, Ito, Yohei, Kiyoshi Takeuchi +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1801.07444

openalex publication_date 2018/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 obtained. Moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original D-modules.

Related

• On Some Topological Properties of Fourier Transforms of Regular Holonomic D-Modules
• Fourier transforms of irregular holonomic D-modules, singularities at infinity of meromorphic functions and irregular characteristic cycles
• A Morse theoretical approach to Fourier transforms of holonomic D-modules in dimension one
• On characteristic cycles of irregular holonomic D-modules
• Regular and irregular holonomic D-modules