On the ideals of secant varieties to certain rational varieties

If X subset of P-n 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=P-n1 x... x P-nt x P-n is the Segre embedding of the product and n is large with respect to the n(i) (Theorem 2.4); the X are some unbalanced Segre-Veronese embeddings; X is a Del Pezzo surface. (c) 2008 Elsevier Inc. All rights reserved.