Secant Varieties of Segre–Veronese Varieties ℙ m × ℙ n Embedded by O(1, 2)

Abstract

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