Blow up for a Holonomic System

Abstract

We introduce a functor that associates to a holonomic system of microdifferential equations $\mathcal{M}$ on a contact manifold $X$ and a closed Lagrangian submanifold $\Lambda$ of $X$ a contact manifold $\tilde{X}$ and a holonomic system $\tilde{\mathcal{M}}$ on $\tilde{X}$. The manifold $\tilde{X}$ is an open set of the blow up of $X$ along a certain ideal of the sheaf of holomorphic functions on $X$. Moreover the restriction of $\mathcal{M}$ to the complementary of $\Lambda$ and the restriction of $\tilde{\mathcal{M}}$ to the complementary of the exceptional divisor of $\tilde{X}$ are isomorphic as systems of microdifferential equations.