Osculating Varieties of Veronesean and their higher secant varieties

Alessandra Bernardi 1 Maria Virgina Catalisano 2 Alessandro Gimigliano 3 Monica Idà 3
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We consider the varieties $O_{k,n.d}$ of the k-osculating spaces to the Veronese varieties, the $d-$uple embeddings of $\PP n$; we study the dimension of their higher secant varieties. Via inverse systems (apolarity) and the study of certain spaces of forms we are able, in several cases, to determine whether those secant varieties are defective or not.
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Alessandra Bernardi, Maria Virgina Catalisano, Alessandro Gimigliano, Monica Idà. Osculating Varieties of Veronesean and their higher secant varieties. Canadian Journal of Mathematics, University of Toronto Press, 2007, 59 (3), pp.488-502. ⟨hal-00646116⟩



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