On the secant varieties to the osculating variety of Veronese surfaces

Abstract. Fix Integers n> 0, k> 0. Here we prove the existence on an integer d(n, k) with the following property. Fix any integer d ≥ d(n, k). Let Ok,n,d ⊂ PN, N:= n+d n) − 1, be the order k osculating variety of the order d Veronese embedding of Pn. Then all the secant varieties of Ok,n,d have the expected dimension