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 $Ysubset mathbb{P}^2$, we find the dimension of $O^s_{k,d}$, the $(s-1)^{th}$secant varieties of $O_{k,d}$, for $3 leq sleq 6$ and $s=9$, and we determine whether those secant varieties are defective or not.
A. Bernardi, M. V. Catalisano (2006). Some defective secant varieties to osculating varieties of Veronese surfaces. COLLECTANEA MATHEMATICA, 57(1), 43-68.
Some defective secant varieties to osculating varieties of Veronese surfaces
BERNARDI, ALESSANDRA;
2006
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 $Ysubset mathbb{P}^2$, we find the dimension of $O^s_{k,d}$, the $(s-1)^{th}$secant varieties of $O_{k,d}$, for $3 leq sleq 6$ and $s=9$, and we determine whether those secant varieties are defective or not.File in questo prodotto:
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