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Testing zero-dimensionality of varieties at a point. (English) Zbl 07363380

Summary: 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 Gröbner systems.

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14H20 Singularities of curves, local rings
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