A new model for the theta divisor of the cubic threefold

Abstract

In this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold X . We use the standard realization of X as a conic bundle and a 4−dimensional family of plane quartics which are totally tangent to the discriminant quintic curve of such a conic bundle structure. The additional data of an even theta characteristic on the curves in the family gives us a model for the theta divisor.