We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to Lê 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.

我们描述了一种新算法，用于计算复杂射影变体的 Whitney 分层。主要成分是 (a) 代数准则，由于 Lê 和 Teissier，它根据共正规空间和映射重新表述了 Whitney 正则性，以及 (b) 通过理想饱和度对这一共正规准则的新解释，它可以在实践中实现一台电脑。我们表明，即使对于相对较小的输入品种，该算法也将现有技术水平提高了几个数量级。在此过程中，我们介绍了用于有效地对仿射品种、给定品种上的标志和代数图进行分层的相关算法。