Advanced Studies in Pure Mathematics

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

Katsusuke Nabeshima and Shinichi Tajima

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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

Source
Singularities in Generic Geometry, S. Izumiya, G. Ishikawa, M. Yamamoto, K. Saji, T. Yamamoto and M. Takahashi, eds. (Tokyo: Mathematical Society of Japan, 2018), 331-344

Dates
Received: 4 July 2016
Revised: 1 March 2017
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538618980

Digital Object Identifier
doi:10.2969/aspm/07810331

Mathematical Reviews number (MathSciNet)
MR3839952

Subjects
Primary: 13D45: Local cohomology [See also 14B15] 32C37: Duality theorems 13J05: Power series rings [See also 13F25] 32A27: Local theory of residues [See also 32C30]

Keywords
limiting tangent space local cohomology

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


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