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 \(\#(S)\le 5\). 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 \(\#(S)= 5\), \(X\cong {\mathbb {P}}^1\times {\mathbb {P}}^1\times {\mathbb {P}}^1\) we use the rational normal curves contained in X.
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The author was partially supported by MIUR and GNSAGA of INdAM (Italy)
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Ballico, E. Linearly dependent subsets of Segre varieties. J. Geom. 111, 23 (2020). https://doi.org/10.1007/s00022-020-00534-7
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DOI: https://doi.org/10.1007/s00022-020-00534-7