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

页码：2005 / 2032

页数：28

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