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

Marco Kuehnel
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Abstract

We describe properties of the Kähler cone of general Calabi-Yau-threefolds with Picard number $ρ(X)=2$ and prove the rationality of the Kähler 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 $c_2(X)$.

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Marco Kuehnel. 2001-10-04. Calabi-Yau-threefolds with Picard number $ρ(X)=2$ and their Kaehler cone I. https://arxiv.org/abs/math/0110054

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