Osculating Varieties of Veronesean and their higher secant varieties

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 determin...

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Bibliographic Details
Published in:Canadian journal of mathematics 2007, Vol.59 (3), p.488-502
Main Authors: Bernardi, Alessandra, Catalisano, Maria Virgina, Gimigliano, Alessandro, Idà, Monica
Format: Article
Language:English
Subjects:
Algebraic Geometry
Commutative Algebra
Mathematics
Online Access:Get full text
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Summary: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.
ISSN:0008-414X