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Some defective secant varieties to osculating varieties of Veronese surfaces.

Alessandra Bernardi; Maria Virginia Catalisano — 2006

Collectanea Mathematica

We consider the k-osculating varietiesO to the Veronese d?uple embeddings of P. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P, we find the dimension of O , the (s?1) secant varieties of O, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.

Segre-Veronese embeddings of P x P x P and their secant varieties.

Maria Virginia Catalisano; Anthony V. Geramita; Alessandro Gimigliano — 2007

Collectanea Mathematica

In this paper we compute the dimension of all the s higher secant varieties of the Segre-Veronese embeddings Y of the product P × P × P in the projective space P via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Y has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.

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