On the ideals of secant varieties to certain rational varieties

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