The Euclidean distance degree of smooth complex projective varieties
Paolo Aluffi and Corey Harris
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Submission date: 02. Aug. 2017
published in: Algebra and number theory, 12 (2018) 8, p. 2005-2032
DOI number (of the published article): 10.2140/ant.2018.12.2005
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.