Conormal Spaces and Whitney Stratifications

TL;DR

This paper introduces a highly efficient algorithm for computing Whitney stratifications of complex projective varieties, leveraging conormal spaces and primary decomposition, significantly outperforming previous methods.

Contribution

It presents a novel algorithm based on algebraic criteria and primary decomposition for Whitney stratification, improving computational efficiency dramatically.

Findings

Algorithm outperforms existing methods by several orders of magnitude

Effective stratification of affine varieties and algebraic maps

Practical implementation demonstrated on various examples

Abstract

We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal spaces and maps, and (b) a new interpretation of this conormal criterion via primary decomposition, 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.