The Kaehler cone of a compact hyperkaehler manifold

摘要

This is an attempt towards the understanding of the (birational) Kaehler coneof a compact hyperkaehler manifold in terms of the Beauville-Bogomolov form onits second cohomology. We discuss birational correspondences betweenhyperkaehler manifolds and their effects on the cohomology. Many of the resultsare conjectural in as much as they depend on a projectivity criterion forcompact hyperkaehler manifolds contained in this paper's predecessor, but inwhich a serious mistake has oocured. An erratum is given in Sect. 6 and a wayto rescue the approach is proposed in Sect. 7.