A note on ED degrees of group-stable subvarieties in polar representations

TL;DR

This paper generalizes a transfer principle that allows the Euclidean distance degree of group-stable subvarieties in polar representations to be computed from their intersections with linear subspaces, extending previous results on matrix varieties.

Contribution

It extends the transfer principle for Euclidean distance degrees to a broader class of group-stable subvarieties in polar representations.

Findings

Generalized the transfer principle to new classes of subvarieties.

Provided methods to compute ED degrees via intersections with linear subspaces.

Enhanced understanding of ED degrees in the context of polar representations.

Abstract

In a recent paper, Drusvyatskiy, Lee, Ottaviani, and Thomas establish a "transfer principle" by means of which the Euclidean distance degree of an orthogonally-stable matrix variety can be computed from the Euclidean distance degree of its intersection with a linear subspace. We generalise this principle.