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 $Ysubset mathbb{P}^n$ 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 Veronese Varieties and Their Higher Secant Varieties / Bernardi, Alessandra; M. V., Catalisano; A., Gimigliano; M., Idà. - In: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. - ISSN 0008-414X. - 59:3(2007), pp. 488-502. [10.4153/CJM-2007-021-6]
Osculating Varieties of Veronese Varieties 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 $Ysubset mathbb{P}^n$ 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.| File | Dimensione | Formato | |
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