Abstract

We prove the rationality of the Kähler cone and the positivity of the Chern class c₂(X) if X is a Calabi–Yau threefold with Picard number ρ(X) = 2 and has an embedding into a Pⁿ-bundle over P^m in the cases (n,m) = (1,3) and (3,1). The case (n,m) = (2,2) has been done in the first part of this paper. Moreover, if (n,m) = (3,1), we describe the ‘other’ contraction different from the projection.

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