Tsukuba Journal of Mathematics

Computation methods of logarithmic vector fields associated to semi-weighted homogeneous isolated hypersurface singularities

Katsusuke Nabeshima and Shinichi Tajima

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Abstract

Methods for computing logarithmic vector fields along a semi-weighted homogeneous hypersurface with an isolated singularity are considered in the context of symbolic computation. The main idea of our approach is based on the concept of polar variety and of algebraic local cohomology. New algorithms are introduced for computing a set of generators of the modules of logarithmic vector fields. The keys of the resulting algorithms are a notion of parametric syzygy system and that of parametric local cohomology system.

Article information

Source
Tsukuba J. Math., Volume 42, Number 2 (2018), 191-231.

Dates
First available in Project Euclid: 2 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1554170422

Digital Object Identifier
doi:10.21099/tkbjm/1554170422

Mathematical Reviews number (MathSciNet)
MR3934988

Subjects
Primary: 32S05: Local singularities [See also 14J17] 32S65: Singularities of holomorphic vector fields and foliations

Keywords
Gröbner bases logarithmic vector fields local cohomology isolated singularities

Citation

Nabeshima, Katsusuke; Tajima, Shinichi. Computation methods of logarithmic vector fields associated to semi-weighted homogeneous isolated hypersurface singularities. Tsukuba J. Math. 42 (2018), no. 2, 191--231. doi:10.21099/tkbjm/1554170422. https://projecteuclid.org/euclid.tkbjm/1554170422


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