Alex Casarotti (Università di Bologna)

Abstract: The classical Waring problem for homogeneous polynomials can be translated into geometric terms, using the notion of defectivity and identifiability for secant varieties. The defectivity problem was completely solved by Alexander-Hirschowitz using degeneracy techniques, in particular the famous "Differential Horace Method". On the other hand identifiability has recently been settled by Mella and Galuppi. In this talk I will briefly explain the relationship between defectivity and identifiability in a more general setting and give bounds for a generalized Waring problem, introduced by Fröberg, Ottaviani and Shapiro. In particular we will see how the union of classical degeneration techniques combine with techniques borrowed from toric geometry, allowing us to give very sharp bounds on identifiability and defectivity.
This is a joint work with Elisa Postinghel.