arXiv subjects

Kazuki Kudomi

Publications and source records attributed to Kazuki Kudomi.

4 recordsLinked to original sources

arXiv2026

Characteristic cycles of real and complex constructible sheaves, revisited

For a smooth morphism $f: X \longrightarrow Σ$ of real analytic manifolds and an $\mathbb{R}$-constructible sheaf $F$ on $X$ satisfying some condition, we define a family of Lagrangian cycles parameterized by $Σ$ that we call the relative characteristic cycle of $F$ for $f$. In this way, the theory of characteristic cycles due to Kashiwara and Schapira is naturally extended to the relative setting. Based on it, we then prove a formula for the characteristic cycles of real nearby cycle sheaves. This leads us to obtain also formulas for the characteristic cycles of various constructible sheaves, such as specialization, microlocalization, and complex nearby and vanishing cycle sheaves, in a unified manner. In fact, our methods allow us to calculate not only their characteristic cycles but also their microlocal types in many situations. We will illustrate it by various examples.

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arXiv2026

On characteristic cycles of irregular holonomic D-modules

Based on the recent progress in the irregular Riemann-Hilbert correspondence for holonomic D-modules, we show that the characteristic cycles of some standard irregular holonomic D-modules can be expressed as in the classical theorem of Ginsburg. For this purpose, we first prove a formula for the enhanced solution complexes of holonomic D-modules having a quasi-normal form, via which, to our surprise, their solution complexes can be calculated more easily by topological methods. In the formulation and the proof of our main theorems, not necessarily homogeneous Lagrangian cycles that we call irregular characteristic cycles will play a crucial role.

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arXiv2025

A Morse theoretical approach to Fourier transforms of holonomic D-modules in dimension one

We study Fourier transforms of holonomic D-modules on the complex 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.e. the stationary phase method. Moreover, we define a Lagrangian cycle that we call the irregular characteristic cycle and describe the enhanced solution complex of the Fourier transform by it. In this way, we obtain a new perspective, from which we can geometrically see how the standard properties of holonomic D-modules are transformed via the Fourier transform. In the course of our study, a formula for the (classical) characteristic cycles of the Fourier transforms will be also obtained and natural bases of their holomorphic solutions will be constructed via rapid decay homology cycles.

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arXiv2024

On the monodromies at infinity of Fourier transforms of holonomic D-modules

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 obtained by applying the theory of monodromy zeta functions to our previous results on the enhanced solution complexes of the Fourier transforms. In particular, in dimension one we thus find a reciprocity law between the monodromies at infinity of holonomic D-modules and their Fourier transforms.

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