Preprint 46/2017

The Euclidean distance degree of smooth complex projective varieties

Paolo Aluffi and Corey Harris

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

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.

06.08.2017, 01:42