The Euclidean distance degree of smooth complex projective varieties

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.

References in corpus (1)

• Tensored Segre classes

Cited by in corpus (4)

• The Distance Function from a Real Algebraic Variety
• Euclidean distance degree and limit points in a Morsification
• On the minimal algebraic complexity of the rank-one approximation problem for general inner products
• Computational complexity of learning algebraic varieties