Some defective secant varieties to osculating varieties of Veronese surfaces
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A. Bernardi
M. V. Catalisano
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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Bernardi, A.; and Catalisano, M. V. “Some defective secant varieties to osculating varieties of Veronese surfaces”. Collectanea Mathematica, vol.VOL 57, no. 1, pp. 43-68, https://raco.cat/index.php/CollectaneaMathematica/article/view/56602.
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