Erratum : Linear projections and successive minima

The proof of Proposition 1 and Theorem 2 in [3] is incorrect. Indeed, §2.5 and §2.7 in op.cit contain a vicious circle: the definition of the filtration Vi, 1 ≤ i ≤ n, in §2.5 depends on the choice of the integers ni, when the definition of the integers ni in §2.7 depends on the choice of the filtration (Vi). Thus, only Theorem 1 and Corollary 1 in [3] are proved. We shall prove below another result instead of Proposition 1 in [3]. I thank J.-B. Bost, C. Gasbarri and C. Voisin for their help.