On the D-module of an isolated singularity

TL;DR

This paper investigates the structure of D-modules generated by powers of 1/f near an isolated hypersurface singularity, linking it to the pole order filtration on the de Rham cohomology of the complement.

Contribution

It provides a detailed description of the D-module generated by powers of 1/f in terms of the pole order filtration, advancing understanding of singularity theory and D-module structures.

Findings

Describes the D-module generated by powers of 1/f near an isolated singularity.

Connects the D-module structure to the pole order filtration on de Rham cohomology.

Offers new insights into the algebraic and analytic properties of hypersurface singularities.

Abstract

Let Z be the germ of a complex hypersurface isolated singularity of equation f, with Z at least of dimension 2. We consider the family of analytic D-modules generated by the powers of 1/f and describe it in terms of the pole order filtration on the de Rham cohomology of the complement of {f=0} in the neighborhood of the singularity.