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Ottaviani, Giorgio
Vietnam journal of mathematics, 07/2022, Letnik: 50, Številka: 3Journal Article
Let q be a nondegenerate quadratic form on V . Let X ⊂ V be invariant for the action of a Lie group G contained in S O ( V , q ). For any f ∈ V consider the function d f from X to ℂ defined by d f ( x ) = q ( f − x ). We show that the critical points of d f lie in the subspace orthogonal to g ⋅ f , that we call critical space. In particular any closest point to f in X lie in the critical space. This construction applies to singular t-ples for tensors and to flag varieties and generalizes a previous result of Draisma, Tocino and the author. As an application, we compute the Euclidean Distance degree of a complete flag variety.
