On the secant varieties of tangential varieties

Let X ⊂ P r be an integral and non-degenerate variety. σ a , b ( ) ⊆ ∈ N 2 the join of copies tangential variety . Using classical Alexander-Hirschowitz theorem (case = 0 recent paper by H. Abo N. Vannieuwenhoven we compute dim ⁡ in many cases when is d -Veronese embedding n This related to certain additive decompositions homogeneous polynomials. We give general proving that expected one Y × 1 has suitable Segre-Veronese style As corollary prove if i ≥ 3 ≤ + 38 embedded | O … not defective similar statement for For arbitrary ample line bundle L on existence integer k such all t with respect ⊗ defective.