We consider the $k$-osculating varieties $O_{k,d}$ to the Veronese $d-$uple embeddings of $\mathbb{P}^{2}$. By studying the Hilbert function of certain zero-\-dimensional schemes $Y\subset \mathbb{P}^2$, we find the dimension of $O^s_{k,d}$, the $(s-1)^{th}$secant varieties of $O_{k,d}$, for $3 \leq s\leq 6$ and $s=9$, and we determine whether those secant varieties are defective or not.
Some defective secant varieties to osculating varieties of Veronese surfaces
BERNARDI, Alessandra;
2006-01-01
Abstract
We consider the $k$-osculating varieties $O_{k,d}$ to the Veronese $d-$uple embeddings of $\mathbb{P}^{2}$. By studying the Hilbert function of certain zero-\-dimensional schemes $Y\subset \mathbb{P}^2$, we find the dimension of $O^s_{k,d}$, the $(s-1)^{th}$secant varieties of $O_{k,d}$, for $3 \leq s\leq 6$ and $s=9$, and we determine whether those secant varieties are defective or not.
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