Elliptic curve configurations on Fano surfaces

Details Elliptic curve configurations on Fano surfaces Elliptic curve configurations on Fano surfaces

2008-04-11

arxiv.org/abs/0804.1861v2

Manus. Math. 129 (2009), no. 3, pp. 381-399

Mathematics

Algebraic Geometry

17 pages, accepted and shortened version, the rest will appear in "Fano surfaces with 12 or 30 elliptic curves"

Scientific paper

10.1007/s00229-009-0264-5

The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That means that we give the number of such curves, their intersections and a plane model. This classification is linked to the classification of the automorphism groups of theses surfaces.

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