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.
Some defective secant varieties to osculating varieties of Veronese surfaces / A. Bernardi; M. V. Catalisano. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - STAMPA. - 57:1(2006), pp. 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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