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arXiv · 1708.00024

The Euclidean distance degree of smooth complex projective varieties

Paolo Aluffi·Corey Harris
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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.

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Paolo Aluffi, Corey Harris. 2017-07-31. The Euclidean distance degree of smooth complex projective varieties. https://doi.org/10.2140/ant.2018.12.2005

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