Preprint 46/2017

The Euclidean distance degree of smooth complex projective varieties

Paolo Aluffi and Corey Harris

Contact the author: Please use for correspondence this email.
Submission date: 02. Aug. 2017
MSC-Numbers: 14C17
Keywords and phrases: Euclidean distance degree, Chern classes, euler characteristic
Link to arXiv:See the arXiv entry of this preprint.

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.

07.06.2018, 00:13