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On the secant varieties to the osculating variety of a Veronese surface

100%

Ballico E., Fontanari C.

Open Mathematics

2003

tom 1

nr 3

315-326

In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.

On the weak non-defectivity of veronese embeddings of projective spaces

100%

Ballico E.

Open Mathematics

2005

tom 3

nr 2

183-187

Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(nn+x). Here we prove that the order x Veronese embedding ofP n is not weakly (k−1)-defective, i.e. for a general S⊃P n such that #(S) = k+1 the projective space | I 2S (x)| of all degree t hypersurfaces ofP n singular at each point of S has dimension (n/n+x )−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I 2S (x)| has an ordinary double point at each P∈ S and Sing (F)=S.

Ograniczanie wyników

2 Open Mathematics

2 Ballico E.

1 Fontanari C.

1 2005

1 2003

Wyniki wyszukiwania

On the secant varieties to the osculating variety of a Veronese surface

On the weak non-defectivity of veronese embeddings of projective spaces