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 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.
翻译:我们描述了计算惠特尼复杂投影品种分层的新算法,主要成分是:(a) 由L ⁇ e和Teissier组成的代数标准,该代数标准根据奇异空间和地图重新定义惠特尼的规律性,以及(b) 通过理想的比喻对这一奇异标准进行新的解释,该比喻可以在计算机上实际应用。我们表明,这一算法在目前水平上提高了几个级,即使是相对较小的投入品种也是如此。在路线上,我们引入了相关的代数法,以便有效地对近亲品种、特定品种的标志和代数地图进行分层。