The Euclidean Distance degree of smooth complex projective varieties

Paolo Aluffi, Corey Harris

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 for- mula
equating the Euclidean distance degree of *X* with the Euler
characteristic of an open subset of *X*.