10 dec 2020 -- 15:00
Applied Algebraic Geometry 2020-2021
To get the access codes for the talk write to elena.angelini@unisi.it.
Abstract.
Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this talk, we present some results concerning the asymptotic behavior of these invariants for various Segre products and their duals. Friedland and Ottaviani found a beautiful formula expressing the number of singular vector tuples of a general tensor. From the formula, one derives the stabilization of the ED degree of Segre varieties, as soon as one of the factors has large enough dimension. We give an alternative viewpoint on this stabilization. Finally, we discuss the stabilization of the degree of the dual variety of the product between a projective variety and a smooth hyperquadric. This is joint work with Giorgio Ottaviani and Luca Sodomaco.