The Critical Space for Orthogonally Invariant Varieties

Abstract Let q be a nondegenerate quadratic form on V . X ⊂ invariant for the action of Lie group G contained in S O ( , ). For any f ∈ consider function d from to $\mathbb C$ ℂ defined by x ) = − We show that critical points lie subspace orthogonal ${\mathfrak g}\cdot f$ g ⋅ f we call space. In particular closest point This construction applies singular t-ples tensors and flag varieties generalizes previous result Draisma, Tocino author. As an application, compute Euclidean Distance degree complete variety.