We consider the $k$-osculating varieties $O_{k,n.d}$ to the (Veronese) $d-$uple embeddings of $\mathbb{P}^{n}$. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes $Y\subset \mathbb{P}^n$ to $O^s_{k,n,d}$ and by studying their Hilbert function we are able, in several cases, to determine whether those secant varieties are defective or not.
Osculating varieties of Veronesean and their higher secant varieties
BERNARDI, Alessandra;
2007-01-01
Abstract
We consider the $k$-osculating varieties $O_{k,n.d}$ to the (Veronese) $d-$uple embeddings of $\mathbb{P}^{n}$. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes $Y\subset \mathbb{P}^n$ to $O^s_{k,n,d}$ and by studying their Hilbert function we are able, in several cases, to determine whether those secant varieties are defective or not.
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