The Euclidean distance degree of smooth complex projective varieties

被引：12
|
作者：
Aluffi, Paolo [1 ]
Harris, Corey [2 ]
机构：
[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA
[2] Max Planck Inst Math Sci, Leipzig, Germany
来源：
ALGEBRA & NUMBER THEORY | 2018年 / 12卷 / 08期
关键词：
algebraic optimization; intersection theory; characteristic classes; Chern-Schwartz-MacPherson classes; CHERN CLASSES;
D O I：
10.2140/ant.2018.12.2005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely simple formula equating the Euclidean distance degree of X with the Euler characteristic of an open subset of X.
引用
收藏
页码：2005 / 2032
页数：28
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