The Fano Surface of the Klein Cubic Threefold
نویسنده
چکیده
We prove that the Klein cubic threefold F is the only one cubic threefold which has an order 11 automorphism. We calculate the period lattice of the intermediate Jacobian of F and study its Fano surface S. We compute the set of fibrations of S on a curve of positive genus and the intersection between the fibres of these fibrations. These fibres generate an index 2 sub-group of the Néron-Severi group and we obtain the generators of this group. The Néron-Severi group of S has rank 25 = h and discriminant 11. MSC: 14J29, 14J50 (primary); 14J70, 32G20 (secondary). Key-words: Fano surface of a cubic threefold, Automorphisms, Surfaces with maximal Picard number. 0.
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