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Cubic fourfolds containing a plane and K3 surfaces of Picard rank two

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Abstract

We present some new examples of families of cubic hypersurfaces in \(\mathbb {P}^5 (\mathbb {C})\) containing a plane whose associated quadric bundle does not have a rational section.

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Acknowledgments

The author would like to thank Bert van Geemen, Edoardo Sernesi and Michele Bolognesi for helpful remarks and useful discussions. The author warmly thanks the referee for the valuable comments which helped to improve the manuscript and for pointing out some mistakes to correct. The author is supported by the framework PRIN 2010/11 “Geometria delle Varietà Algebriche”, cofinanced by MIUR. Member of GNSAGA.

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  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto n.10, 10123, Turin, Italy

    Federica Galluzzi

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  1. Federica Galluzzi
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Correspondence to Federica Galluzzi.

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Galluzzi, F. Cubic fourfolds containing a plane and K3 surfaces of Picard rank two. Geom Dedicata 186, 103–112 (2017). https://doi.org/10.1007/s10711-016-0181-1

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  • DOI: https://doi.org/10.1007/s10711-016-0181-1

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