### 2002-25

#### Calabi-Yau-threefolds with Picard number rho(X)=2 and their Kaehler cone II

by Kuehnel, M..

Series: 2002-25, Preprints

MSC:
14J30 $3$-folds

Abstract:
We prove the rationality of the Kaehler cone and the positivity of $c_2(X)$, if $X$ is a Calabi-Yau-threefold with $\rho(X)=2$ and has an embedding into a
${\bb P}^n$-bundle over ${\bb P}^m$ in the cases $(n,m)=(1,3),(3,1)$. 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.

Keywords:
Calabi-Yau-3-folds