Evento
Descrizione:
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, such as the famous ”differential Horace method”. On the other hand (generic)
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 Fr¨oberg, 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. In the last part of the talk I will show how to generalize this approach to various types of toric varieties.
This is a joint work with Elisa Postinghel.
