On Completeness and Linear Dependence for Differential Algebraic Varieties
نویسنده
چکیده
In this paper we deal with two foundational questions on complete differential algebraic varieties. We establish, by means of the differential algebraic version of Bertini’s theorem and assuming a weaker form of the catenary conjecture, that in order to verify (differential) completeness one can restrict second factors to zero-dimensional differential varieties. Then, we extend Kolchin’s results from [11] on linear dependence over projective varieties in the constants, to linear dependence over arbitrary complete differential varieties.
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