Gröbner Fan for Analytic D-modules with Parameters

Generic Gröbner Bases: Application to the Constructibility of the Set of the Algebraic and Analytic Gröbner Fans

The contribution of this paper lies in two aspects. The first one deals with a natural notion of generic Gröbner (or standard) bases on an irreducible affine scheme for an ideal depending on parameters. This takes place in rings of differential operators and concerns the algebraic and the formal case. This gives a generalization of some results of V. Weispfenning obtained in a commutative and a...

Generic Gröbner Bases in D-modules and Application to Algebraic and Analytic Gröbner Fans

The contribution of this paper lies in two aspects. The first one deals with a natural notion of generic Gröbner (or standard) bases on an irreducible affine scheme for an ideal depending on parameters. This takes place in rings of differential operators and concerns the algebraic and the formal case. Thus we obtain a generalization of some known results in polynomial rings. The second aspect i...

Local Gröbner fan

This note summarizes results concerning local Gröbner fans. Any Gröbner fan of an ideal in a power series ring, or in an analytic or formal differential operator ring, is found to be a polyhedral fan. We also compare the notions of global and local Gröbner fans, and discuss applications of our results. To cite this article: R. Bahloul, N. Takayama, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

A Flatness Property for Filtered D-modules

Let M be a coherent module over the ring DX of linear differential operators on an analytic manifold X and let Z1, · · · , Z k be k germs of transverse hypersurfaces at a point x ∈ X. The Malgrange-Kashiwara V-filtrations along these hypersurfaces, associated with a given presentation of the germ of M at x, give rise to a multifiltration U • (M) of Mx as in Sabbah's paper [9] and to an analytic...

Projective modules over polynomial rings and dynamical Gröbner bases