For a holonomic D-module M on a complex manifold X, we define the conic Lagrangian cycle CC(M) on the cotangent bundle T*X.
This cycle is called the characteristic cycle of M.
Building on the theory of meromorphic connections developed by Sabbah, Mochizuki and Kedlaya, D’Agnolo–Kashiwara established the Riemann–Hilbert correspondence for (not necessarily regular) holonomic D-modules.
In this talk, as an application of this correspondence, we calculate the characteristic cycles for some irregular holonomic D-modules and give a generalization of Ginzburg’s formula for the limit of characteristic cycles.
This talk is based on joint work with Kiyoshi Takeuchi.