Monodromy Structure of Solutions of Holonomic Systems of Linear Differential Equations is Invariant under the Deformation of the System

Inspired by some physical problems, Sato has recently proposed to investigate the deformation of systems of (micro-) differential equations with the emphasis on the in variance of global character of solutions. (Sato et al. [4]) Especially, he has observed that the classical result of Schlesinger [5] is most neatly explained from this point of view. The purpose of this note is to show that the monodromy structure of solutions of holonomic systems of linear differential equations is invariant under the deformation of the system specified below (Definition 1) on the condition that related topological structure does not change. (See Corollary 1 for the precise statement.) We first list up some notations used in this note. We refer the reader to S-K-K [3] for notations not listed here. X: a complex maniford. A point in X shall be denoted by x. 7t: the projection map from T*X to X. U: a connected Stein open set in CN. A point in CN shall be denoted by *=(*i, —,**)• Xc={c}xXc:UxX for c^U. The natural injection from Xc to UxX shall be denoted by cc. We sometimes identify Xc with X.