Blow up for a Holonomic System

Abstract

We introduce a functor that associates to a holonomic system of microdifferential equations M on a contact manifold X and a closed Lagrangian submanifold Λ of X a contact manifold ~X and a holonomic system ~M on ~X. The manifold ~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 M to the complementary of Λ and the restriction of ~M to the complementary of the exceptional divisor of ~X are isomorphic as systems of microdifferential equations.