Erratum to: Compact hyperkähler manifolds: basic results (Q1396680)

Concerns the author's paper in ibid. 135, 63-113 (1999; Zbl 0953.53031). It was pointed out by D. Kaledin that the proof of Proposition 3.8 is wrong. Actually, the proposition itself cannot be true as we explain here. It was used to prove Corollary 3.10 and Theorem 3.11. The latter is the so-called projectivity criterion for hyper-Kähler manifolds. Here we give a correct proof of these two results. The main input is a recent theorem of \textit{J.-P. Demailly} and \textit{M. Paun} [Ann. Math. (2) (to appear), see also math.AG/0105176]. All the other results of the paper remain unaffected.