Displaying similar documents to “Some defective secant varieties to osculating varieties of Veronese surfaces.”

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

Maria Virginia Catalisano, Anthony V. Geramita, Alessandro Gimigliano (2007)

Collectanea Mathematica

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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.

Special effect varieties in higher dimension.

Cristiano Bocci (2005)

Collectanea Mathematica

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Here we introduce the concept of special effect varieties in higher dimension and we generalize to P, n ≥ 3, the two conjectures given in [2] for the planar case. Finally, we propose some examples on the product of projective spaces and we show how these results fit with the ones of Catalisano, Geramita and Gimigliano.