论文标题
欧几里得距离度和限制点
Euclidean distance degree and limit points in a Morsification
论文作者
论文摘要
通过找到一种有效的方法来计算代数模型最近点问题的代数复杂性的动机，我们引入了一种有效的方法，用于检测分层摩尔斯的轨迹的极限点，以对复杂仿射品种的任何多项式功能的小扰动。我们根据消失的周期来计算这些极限点的多重性。对于仅具有孤立的分层奇点的函数，我们以极性相交数来表达局部多重性。
Motivated by finding an effective way to compute the algebraic complexity of the nearest point problem for algebraic models, we introduce an efficient method for detecting the limit points of the stratified Morse trajectories in a small perturbation of any polynomial function on a complex affine variety. We compute the multiplicities of these limit points in terms of vanishing cycles. In the case of functions with only isolated stratified singularities, we express the local multiplicities in terms of polar intersection numbers.
