On linear dependence over complete differential algebraic varieties

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We extend Kolchin's results from [12 Kolchin, E. (1974). Differential equations in a projective space and linear dependence over a projective variety. Contributions to analysis (A collection of papers dedicated to Lipman Bers). Cambridge, MA: Academic Press, pp. 195–214.[CrossRef]] on linear dependence over the constant points of projective algebraic varieties to linear dependence over arbitrary complete differential algebraic varieties. We show that in this more general setting, the notion of linear dependence still has necessary and sufficient conditions given by the vanishing of a certain system of differential-polynomials equations. We also discuss some conjectural questions around completeness and the catenary problem.

Bibliographical metadata

Original languageEnglish
Pages (from-to)2645-2669
JournalCommunications in Algebra
Issue number6
Early online date15 Jul 2015
StatePublished - 2016