Indexed on: 07 Feb '08Published on: 07 Feb '08Published in: Mathematics - Algebraic Geometry
Let X be a smooth cubic threefold. We can associate two objects to X: the intermediate Jacobian J and the Fano surface F parametrising lines on X. By a theorem of Clemens and Griffiths, the Fano surface can be embedded in the intermediate Jacobian and the cohomology class of its image is minimal. In this paper we show that if X is generic, the Fano surface is the only surface of minimal class in J.