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Article Dans Une Revue Journal of Mathematics of Kyoto University Année : 2009

The Fano surface of the Klein cubic threefold

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Résumé

We prove that the Klein cubic threefold FF is the only smooth cubic threefold which has an automorphism of order 1111. We compute the period lattice of the intermediate Jacobian of FF and study its Fano surface SS. We compute also the set of fibrations of SS onto a curve of positive genus and the intersection between the fibres of these fibrations. These fibres generate an index 22 sub-group of the Néron-Severi group and we obtain a set of generators of this group. The Néron-Severi group of SS has rank 25=h1,125=h^{1,1} and discriminant 111011^{10}.

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Dates et versions

hal-03054032 , version 1 (11-12-2020)

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  • HAL Id : hal-03054032 , version 1
  • OKINA : ua188

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Xavier Roulleau. The Fano surface of the Klein cubic threefold. Journal of Mathematics of Kyoto University, 2009, 49 (1), pp.113 - 129. ⟨hal-03054032⟩
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