### 2002-24

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

by Kuehnel, M..

Series: 2002-24, Preprints

MSC:
14J30 $3$-folds

Abstract:
We describe properties of the Kaehler cone of general Calabi-Yau-threefolds with Picard number $\rho(X)=2$ and prove the rationality of the Kaehler cone, if $X$ is
a Calabi-Yau-hypersurface in a ${\mathbb P}^2$-bundle over ${\mathbb P}^2$ and $c_3(X)\le -54$. Without the latter assumption we prove the positivity of $c_2(X)$.

Keywords:
Calabi-Yau-3-folds