Osculating Varieties of Veronesean and their higher secant varieties

Details Osculating Varieties of Veronesean and their higher secant varieties Osculating Varieties of Veronesean and their higher secant varieties

2004-03-08

arxiv.org/abs/math/0403132v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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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