On characteristic cycles of irregular holonomic D-modules

Kazuki Kudomi; Kiyoshi Takeuchi

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arXiv · 2503.10090

On characteristic cycles of irregular holonomic D-modules

Kazuki Kudomi·Kiyoshi Takeuchi

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Abstract

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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Kazuki Kudomi, Kiyoshi Takeuchi. 2025-03-13. On characteristic cycles of irregular holonomic D-modules. https://arxiv.org/abs/2503.10090

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