A new method for computing the limiting tangent space of an isolated hypersurface singularity via algebraic local cohomology

Abstract

Limiting tangent hyperplanes associated with isolated hypersurface singularities are considered in the context of symbolic computation. A new effective method is proposed to compute the limiting tangent space of a given hypersurface. The key of the method is the concept of parametric local cohomology systems. The proposed method can provide the decomposition of the limiting tangent space by Milnor numbers of hyperplane sections of a given hypersurface. The resulting algorithm has been implemented in the computer algebra system $\mathsf{Risa/Asir}$. Examples of the computation for some typical cases are given.