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.

Article information

Dates
Revised: 1 March 2017
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538618980

Digital Object Identifier
doi:10.2969/aspm/07810331

Mathematical Reviews number (MathSciNet)
MR3839952

Zentralblatt MATH identifier
1420.13044

Citation

Nabeshima, Katsusuke; Tajima, Shinichi. A new method for computing the limiting tangent space of an isolated hypersurface singularity via algebraic local cohomology. Singularities in Generic Geometry, 331--344, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07810331. https://projecteuclid.org/euclid.aspm/1538618980