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

Marco Kuehnel

Published 2001-10-04Version 1

We describe properties of the K\"ahler cone of general Calabi-Yau-threefolds with Picard number $\rho(X)=2$ and prove the rationality of the K\"ahler 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 $c_2(X)$.