Testing zero-dimensionality of varieties at a point
Symbolic Computation
2019-04-01 v1
Abstract
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing local dimensions are also described. For the case where a given ideal contains parameters, the proposed algorithms can output in particular a decomposition of a parameter space into strata according to the local dimension at a point of the associated varieties. The key of the proposed algorithms is the use of the notion of comprehensive Gr\"obner systems.
Cite
@article{arxiv.1903.12365,
title = {Testing zero-dimensionality of varieties at a point},
author = {Katsusuke Nabeshima and Shinichi Tajima},
journal= {arXiv preprint arXiv:1903.12365},
year = {2019}
}