Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

Bernardi, A. ; Catalisano, M. V. ; Gimigliano, A. ; Idà, M.

Canadian journal of mathematics, Tome 59 (2007) no. 3, pp. 488-502

Résumé

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 $O_{k,n,d}^{s}$ and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.

Détail

DOI : 10.4153/CJM-2007-021-6

Mots-clés : 14N15, 15A69

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