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

Marco Kuehnel
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Abstract

We prove the rationality of the Kähler cone and the positivity of $c_2(X)$, if $X$ is a Calabi-Yau-threefold with $ρ(X)=2$ 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.

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Marco Kuehnel. 2002-01-30. Calabi-Yau-threefolds with Picard number $ρ(X)=2$ and their Kaehler cone II. https://arxiv.org/abs/math/0201295

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