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Conormal Spaces and Whitney Stratifications.

CAS-2 JCR-Q1 SCIE EI
Martin HelmerVidit Nanda
Foundations of Computational Mathematics
Jun 2021
摘要
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to Le and Teissier, which reformulates Whitney regularity in terms of conormal spaces and maps, and (b) a new interpretation of this conormal criterion via ideal saturations, which can be practically implemented on a computer. We show that this algorithm improves upon the existing state of the art by several orders of magnitude, even for relatively small input varieties. En route, we introduce related algorithms for efficiently stratifying affine varieties, flags on a given variety, and algebraic maps.
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