The analytic standard fan of a D-module

Abstract

We extend to the analytic D-module case our results in the algebraic case, namely, we associate with any monogeneous module over the ring D of germs of linear differential operators at the origin of Cn, with holomorphic coefficients, a combinatorial object which we call the standard fan of this D-module (see chapter 6 for a precise geometric description of this object). The main tool of the proof is the homogenization techniques and a convergent division theorem that we prove in the homogenization ring D[t].