Osculating Varieties of Veronesean and their higher secant varieties

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

Osculating Varieties of Veronesean and their higher secant varieties

Algebraic Geometry 2007-05-23 v1 Commutative Algebra

Authors: A. Bernardi , M. V. Catalisano , A. Gimigliano , M. Idà

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.

Keywords

osculating varieties veronese varieties higher secant varieties defectiveness inverse systems apolarity

Cite

@article{arxiv.math/0403132,
  title  = {Osculating Varieties of Veronesean and their higher secant varieties},
  author = {A. Bernardi and M. V. Catalisano and A. Gimigliano and M. Idà},
  journal= {arXiv preprint arXiv:math/0403132},
  year   = {2007}
}

Comments

12 pages

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