Calabi–Yau threefolds with Picard number ρ(X) = 2 and their Kähler cone II

We prove the rationality of the Khler cone and the positivity of the Chern class c 2 (X) if X is a Calabi-Yau threefold with Picard number (X) = 2 and has an embedding into a P n -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.