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 τ 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 τV(f_1,..., f_s) 6= V(f_1..., f_s, τf_1,..., τf_s). But a different, indeed simpler, set of first-order axioms, which we will now describe, does express the geometric characterization.

.A small error in the paper is corrected