Advanced Search

In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.

Let $Y$ be an integral projective curve with $g:=p_a\left(Y\right)\ge 2$. For all positive integers $d$, $r$ let $W_d^r\left(Y\right)\left({}^{*A*}\right)$ be the set of all $L\in {\text{Pic}}^d\left(Y\right)$ with $h^0\left(Y,L\right)\ge r+1$ and $L$ spanned. Here we prove that if $d\le g-2$, then $dim\left(W_d^r\left(Y\right)\left({}^{*A*}\right)\right)\le d-3r$ except in a few cases (essentially if $Y$ is a double covering).