Algebraic Local Cohomology Classes Attached to Unimodal Singularities

Abstract

Algebraic local cohomology classes and holonomic systems attached to non-quasihomogeneous isolated unimodal singularities are considered in the context of algebraic analysis. Holonomic systems and their algebraic local cohomology solution spaces attached to a unimodal singularity are studied in a constructive manner. The holonomic system constructed from linear partial differential operators of order at most two that annihilate the given algebraic local cohomology is proven to be simple for the case of non-quasihomogeneous unimodal singularities.