On the ideals of secant varieties to certain rational varieties

If X⊂Pn is a reduced and irreducible projective variety, it is interesting to find the equations describing the (higher) secant varieties of X. In this paper we find those equations in the following cases:
• X=Pn1×⋯×Pnt×Pn is the Segre embedding of the product and n is “large” with respect to the ni (Theorem 2.4);
• the X are some “unbalanced” Segre–Veronese embeddings;
• X is a Del Pezzo surface.