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 (7)

• Chern classes for singular hypersurfaces
• Computing characteristic classes of projective schemes
• An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties
• Euler characteristics of general linear sections and polynomial Chern classes
• A method to compute Segre classes of subschemes of projective space
• Projective duality and a Chern-Mather involution
• 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