Differential Chow varieties exist

The Chow variety is a parameter space for effective algebraic cycles on Pn (or An ) of given dimension and degree. We construct its analog for differential algebraic cycles on An , answering a question of Gao, Li and Yuan [Trans. Amer. Math. Soc. 365 (2013) 4575–4632]. The proof uses the construction of classical algebro‐geometric Chow varieties, the theory of characteristic sets of differential varieties and algebraic varieties, the theory of prolongation spaces and the theory of differential Chow forms. In the course of the proof, several definability results from the theory of algebraically closed fields are required. Elementary proofs of these results are given in the appendix.

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