Secant Varieties of (P ^1) X .... X (P ^1) (n-times) are NOT Defective for n \geq 5

A.Geramita; A.Gimigliano; M.V.Catalisano

arxiv: 0809.1701 · v1 · submitted 2008-09-10 · 🧮 math.AG · math.AC

Secant Varieties of (P ¹) X .... X (P ¹) (n-times) are NOT Defective for n geq 5

M.V.Catalisano , A.Geramita , A.Gimigliano This is my paper

classification 🧮 math.AG math.AC

keywords dimensionexpectedsecantsigmavarietiesalwaysdefectiveembedding

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Let V_n be the Segre embedding of (P^1) x ... X (P^1) (n times). We prove that the higher secant varieties, \sigma_s(V_n), always have the expected dimension, except for \sigma_3(V_4), which is of dimension 1 less than expected.

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Secant Varieties of (P ¹) X .... X (P ¹) (n-times) are NOT Defective for n geq 5

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