Ettore Teixera Turatti: Terracini locus and special points configuration

Abstract.

Let \(X\) be a nondegenerate projective variety. Terracini's Lemma is a classical result that describes the tangent space to the secant varieties of \(X\) at a generic point. However, it does not characterise which points in the secant variety are generic. Therefore, an interesting question is to determine the special configurations of points for which Terracini's Lemma fails, or in other words, when zero-dimensional schemes of double points supported on \(X\) do not impose independent conditions. In this talk, we will focus on this question in the case of curves and Veronese varieties. This is joint work with Francesco Galuppi, Pierpaola Santarsiero, and Douglas Torrence.