Abstract
This paper is a sequel to [11]. We study a number of questions only touched upon in [11] in more detail. In particular: What is the relation between two birational compact hyperkähler manifolds? What is the shape of the cone of all Kähler classes on such a manifold? How can the birational Kähler cone be described? Most of the results are motivated by either the well-established two-dimensional theory, i.e. the theory of K3 surfaces, or the theory of Calabi-Yau threefolds and string theory.
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