Secant Varieties of Segre–Veronese Varieties ℙ^<i>m</i>× ℙ^<i>n</i>Embedded by<i>O</i>(1, 2)

Abstract

Let X m,n be the Segre–Veronese variety ℙ m × ℙ n embedded by the morphism given by O(1, 2). In this paper, we provide two functions such that the sth secant variety of X m,n has the expected dimension if or . We also present a conjecturally complete list of defective secant varieties of such Segre–Veronese varieties.