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

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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 ℙ2-bundle over ℙ2 and c 3 (X)≤−54. Without the latter assumption we prove the positivity of c 2 (X).

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Bayreuth, 95440, Bayreuth, Germany

    Marco Kühnel

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  1. Marco Kühnel
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The author acknowledges gratefully support by the DFG priority program ‘Global Methods in Complex Geometry’.

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Kühnel, M. Calabi-Yau-threefolds with Picard number ρ(X)=2 and their Kähler cone I. Math. Z. 245, 233–254 (2003). https://doi.org/10.1007/s00209-003-0540-0

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  • DOI: https://doi.org/10.1007/s00209-003-0540-0

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