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# Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

Published:2007-06-01
Printed: Jun 2007
• A. Bernardi
• M. V. Catalisano
• A. Gimigliano
• M. Idà
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## Abstract

We consider the $k$-osculating varieties $O_{k,n.d}$ to the (Veronese) $d$-uple embeddings of $\PP^n$. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes $Y\subset \PP^n$ to $O^s_{k,n,d}$ and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.
 MSC Classifications: 14N15 - Classical problems, Schubert calculus 15A69 - Multilinear algebra, tensor products