## Algebra & Number Theory

### The Euclidean distance degree of smooth complex projective varieties

#### Abstract

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 $X$.

#### Article information

Source
Algebra Number Theory, Volume 12, Number 8 (2018), 2005-2032.

Dates
Received: 3 November 2017
Revised: 3 May 2018
Accepted: 19 June 2018
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ant/1545361468

Digital Object Identifier
doi:10.2140/ant.2018.12.2005

Mathematical Reviews number (MathSciNet)
MR3892971

Zentralblatt MATH identifier
06999508

#### Citation

Aluffi, Paolo; Harris, Corey. The Euclidean distance degree of smooth complex projective varieties. Algebra Number Theory 12 (2018), no. 8, 2005--2032. doi:10.2140/ant.2018.12.2005. https://projecteuclid.org/euclid.ant/1545361468

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