On systems with regular singularities, and their solutions

V. A. Golubeva

Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 27-38

Résumé

In this article two problems are solved. 1. It is shown that there exists an exponential representation for the fundamental matrix of a Pfaffian system on $C^n$ with regular singularities on a reducible algebraic submanifold $L$. 2. Let there be given on an algebraic manifold $X$ a function $f(x)$ of the Nilsson class with branch manifold $L\subset X$. It is shown that in a neighborhood of an ordinary point or of a point of normal intersection of components of $L$ the function $f(x)$ generates a $\mathscr D_X$-module with regular singularities on $L$. Bibliography: 28 titles.