Corrigendum to the paper: Geometric Axioms for Differentially Closed Fields with Several Commuting Derivations

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In the proof of Lemma 2.6 (2) the iteration of the map τ was not performed properly and in fact the lemma is wrong; a counterexample is given by f = x₁and k = 2. This error does not, however, affect the geometric characterization given in Theorem 3.4 but only the attempt in Theorem 4.3 to express it as a first-order set of axioms. That attempt is incorrect; the main problem being that in general τV(f₁,..., fₛ) 6= V(f₁..., fₛ, τf₁,..., τfₛ). But a different, indeed simpler, set of first-order axioms, which we will now describe, does express the geometric characterization.