The determinantal ideals of extended Hankel matrices

In this paper, we use the tools of Grobner bases and combinatorial secant varieties to study the determinantal ideals I-t of the extended Hankel matrices. Denote by c-chain a sequence a(1), . . . , a(k) with a(i) + c < a(i+1) for all i = 1, . . ., k - 1. Using the results of c-chain, we solve the membership problem for the symbolic powers I-t((s)) and we compute the primary decomposition of the product I-t1, . . . I-tk of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product I-t1, . . . .I-tk has a linear resolution and the multi-homogeneous Rees algebra Rees(I-t1, . . . , I-tk) is defined by a Grobner basis of quadrics. (C) 2010 Elsevier B.V. All rights reserved.