Algorithmic Tests for the Normal Crossing Property

Given a finite set of varieties in some nonsingular affine variety W. They are normal crossing if and only if at every point of W there is a regular system of parameters such that each variety can be defined locally at the point by a subset of this parameter system. In this paper we present two algo...

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1. Verfasser: BODNAR, Gabor
Format: Buchkapitel
Sprache:eng
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Zusammenfassung:Given a finite set of varieties in some nonsingular affine variety W. They are normal crossing if and only if at every point of W there is a regular system of parameters such that each variety can be defined locally at the point by a subset of this parameter system. In this paper we present two algorithms to test this property. The first one is developed for hypersurfaces only, and it has a straightforward structure. The second copes with the general case by constructing finitely many regular parameter systems which are “witnesses” of the normal crossing of the varieties over open subsets of W. The ideas of the methods are applied in a computer program for resolution of singularities.
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-24616-9_1