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

Abstract

In the proof of Lemma 2.6 (2) the iteration of the map {\tau} was not performed properly and in fact the lemma is wrong; a counterexample is given by f = \bar{x}_1and 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 {\tau}V(f_1,..., f_s) 6= V(f_1..., f_s, {\tau}f_1,..., {\tau}f_s). But a different, indeed simpler, set of first-order axioms, which we will now describe, does express the geometric characterization.