The analytic standard fan of a D-module

In this paper, we associate with any monogeneous module over the ring D of germs of linear differential operators at the origin of C-n, with holomorph ic coefficients, a combinatorial object which we call the standard fan of t his D-module (see Section 6 for a precise geometric description of this obj ect). The main tool of the proof is the homogenization technique and a conv ergent division theorem in the homogenization ring D[t]. This last result i s the key tool to an extension to the analytic D-module case of our results in the algebraic case of the Weyl algebra (see Assi et al., J. Pure Appl. Algebra, 150 (1) (2000) 27-39. (C) 2001 Elsevier Science B.V. All rights re served.