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Some defective secant varieties to osculating varieties of Veronese surfaces

Alessandra Bernardi 1 Maria Virgina Catalisano 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We consider the $k$-osculating varieties $O_{k,d}$ to the Veronese $d-$uple embeddings of $\PP 2$. By studying the Hilbert function of certain zero-\-dimensional schemes $Y\subset \PP 2$, 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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Alessandra Bernardi, Maria Virgina Catalisano. Some defective secant varieties to osculating varieties of Veronese surfaces. Collectanea Mathematica, University of Barcelona / Springer Verlag, 2006, 57 (1), pp.43-68. ⟨hal-00645929⟩

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