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

Marco Kühnel

Vol. 217 (2004), No. 1, 115–137

DOI: 10.2140/pjm.2004.217.115

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.

Milestones

Received: 8 November 2002

Revised: 15 January 2003

Published: 1 November 2004