On the ideals and singularities of secant varieties of Segre varieties

Abstract

We find minimal generators for the ideals of secant varieties of Segre varieties in the cases of σk(ℙ1 × ℙn × ℙm) for all k, n, m, σ2(ℙn × ℙm × ℙp × ℙr) for all n, m, p, r (GSS conjecture for four factors), and σ3(ℙn × ℙm × ℙp) for all n, m, p and prove they are normal with rational singularities in the first case and arithmetically Cohen–Macaulay in the second two cases.