(1) Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
Abstract:
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.