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arXiv · 1903.12365

Testing zero-dimensionality of varieties at a point

Katsusuke Nabeshima·Shinichi Tajima
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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.

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Katsusuke Nabeshima, Shinichi Tajima. 2019-03-29. Testing zero-dimensionality of varieties at a point. https://arxiv.org/abs/1903.12365

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