We study the linear algebra of finite subsets S of a Segre variety X. In particular we classify the pairs (S, X) with S linear dependent and #(S)≤5. We consider an additional condition for linear dependent sets, i.e. that no two of their points are contained in a line of X, and get far better lower bounds for #(S) in term of the dimension and number of the factors of X. In this discussion and in the classification of the case #(S)=5, X≅P1×P1×P1 we use the rational normal curves contained in X.
Linearly dependent subsets of Segre varieties / Ballico, Edoardo. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - STAMPA. - 2020, 111:2(2020), pp. 23.1-23.19. [10.1007/s00022-020-00534-7]
Linearly dependent subsets of Segre varieties
Ballico, Edoardo
2020-01-01
Abstract
We study the linear algebra of finite subsets S of a Segre variety X. In particular we classify the pairs (S, X) with S linear dependent and #(S)≤5. We consider an additional condition for linear dependent sets, i.e. that no two of their points are contained in a line of X, and get far better lower bounds for #(S) in term of the dimension and number of the factors of X. In this discussion and in the classification of the case #(S)=5, X≅P1×P1×P1 we use the rational normal curves contained in X.| File | Dimensione | Formato | |
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