Euclidean Distance Degree of secant varieties of the Veronese variety

Compute the Euclidean Distance Degree, with respect to the Bombieri–Weyl product, of the r-th secant variety of the Veronese variety V for every r\ge 2.

Background

The computation of the Euclidean Distance Degree of the tangential variety is presented as a first step toward the corresponding problem for secant varieties of the Veronese variety. The paper states that the general secant-variety problem is largely open, with results available only in selected cases such as matrices and low secant orders of rational normal curves.