Algebraic Local Cohomology Classes Attached to Quasi-Homogeneous Hypersurface Isolated Singularities

Abstract

The purpose of this paper is to study hypersurface isolated singularities by using partial differential operators based on $\mathcal{D}$-modules theory. Algebraic local cohomology classes supported at a singular point that constitute the dual space of the Milnor algebra are considered. It is shown that an isolated singularity is quasi-homogeneous if and only if an algebraic local cohomology class generating the dual space can be characterized as a solution of a holonomic system of first order partial differential equations.