manuscripta mathematica

, Volume 129, Issue 3, pp 381-399

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Elliptic curve configurations on Fano surfaces

  • Xavier RoulleauAffiliated withGraduate School of Mathematical Sciences, The University of Tokyo Email author 


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.

Mathematics Subject Classification (2000)

Primary 14J29 Secondary 14J45 14J50 14J70 32G20