On non-defectivity of certain Segre-Veronese varieties

Let Xm,n be the Segre-Veronese variety Pm ×Pn embedded by the morphism given by O(1, 2) and let σs(Xm,n) denote the sth secant variety to Xm,n. In this paper, we prove that if m = n or m = n+1, then σs(Xm,n) has the expected dimension except for σ6(X4,3). As an immediate consequence, we will give function s1(m, n) ≤ s2(m, n) such that if s ≤ s1(m, n) or if s ≥ s2(m, n), then σs(Xm,n) has the expected dimension.

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Hirotachi Abo
• Keywords: Dimension, Immediate Consequence, JSC 2010, Segre-veronese Variety Pm