Secant varieties to osculating varieties of Veronese embeddings of P^n

@inproceedings{Bernardi2009SecantVT,
  title={Secant varieties to osculating varieties of Veronese embeddings of P^n},
  author={Alessandra Bernardi and Maria Virginia Catalisano and Alessandro Gimigliano and Monica Id{\`a}},
  year={2009}
}
A well known theorem by Alexander-Hirschowitz states that all the higher secant varieties of $V_{n,d}$ (the $d$-uple embedding of $\PP n$) have the expected dimension, with few known exceptions. We study here the same problem for $T_{n,d}$, the tangential variety to $V_{n,d}$, and prove a conjecture, which is the analogous of Alexander-Hirschowitz theorem, for $n\leq 9$. Moreover. we prove that it holds for any $n,d$ if it holds for $d=3$. Then we generalize to the case of $O_{k,n,d}$, the $k… CONTINUE READING