2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70462In 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.Algebraic Geometry14H10, 14H40, 14H50text