Resumen de On the dimension of secant varieties

Luca Chiantini, Ciro Ciliberto

• In this paper we generalize Zak�s theorems on tangencies and on linear normality as well as Zak�s definition and classification of Severi varieties. In particular we find sharp lower bounds for the dimension of higher secant varieties of a given variety X under suitable regularity assumptions on X, and we classify varieties for which the bound is attained.