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

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

2001-10-04

arxiv.org/abs/math/0110054v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

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 $c_2(X)$.

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