Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

http://dx.doi.org/10.4153/CJM-2007-021-6
Canad. J. Math. 59(2007), 488-502

  Published:2007-06-01
 Printed: Jun 2007

We consider the $k$-osculating varieties $O_{k,n.d}$ to the (Veronese) $d$-uple embeddings of $\PP^n$. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes $Y\subset \PP^n$ to $O^s_{k,n,d}$ and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.