The Kaehler cone of a compact hyperkaehler manifold

Abstract

This is an attempt towards the understanding of the (birational) Kaehler cone of a compact hyperkaehler manifold in terms of the Beauville-Bogomolov form on its second cohomology. We discuss birational correspondences between hyperkaehler manifolds and their effects on the cohomology. Many of the results are conjectural in as much as they depend on a projectivity criterion for compact hyperkaehler manifolds contained in this paper's predecessor, but in which a serious mistake has oocured. An erratum is given in Sect. 6 and a way to rescue the approach is proposed in Sect. 7.

This is a major revision of the paper. All results based on the projectivity criterion for hyperkahler manifolds have a complete proof now (see the Erratum in alg-geom/9705025). The sections on the Beauville-Bogomolov form are omitted in this version. Further corrections are made in Sect. 1 and 4

References in corpus (1)

• Beyond the Kähler cone

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