Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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The ED polynomial of the dual varieties of Veronese varieties

Luca Sodomaco

created by angelini on 24 Dec 2018

16 jan 2019 -- 12:00

Sala Tricerri, DiMaI, Firenze

Abstract.

In the first part of this talk, we outline the main properties of the ED polynomial of a real algebraic variety, where ED stands for "Euclidean Distance". Then we focus on the ED polynomial of the dual of the d-th Veronese variety of Pn, showing its close relationship with the spectral theory of symmetric tensors. In particular, we investigate its lowest and highest coefficients and their corresponding vanishing loci. The main result is a closed formula for the product of the Euclidean eigenvalues of a symmetric tensor, which generalizes the known fact that the determinant of a symmetric matrix is the product of its eigenvalues.

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