The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold

The Abel-Jacobi map of the family of elliptic quintics lying on a general c ubic threefold is studied. It is proved that this map factors through a mod uli component of stable rank 2 vector bundles on the cubic threefold with C hern numbers c(1) = O, c(2) = 2, whose general point represents a vector bu ndle obtained by Serre's construction from an elliptic quintic. The ellipti c quintics mapped to a point of the moduli space vary in a 5-dimensional pr ojective space inside the Hilbert scheme of curves, and the map from the mo duli space to the intermediate Jacobian is etale. As auxiliary results, the irreducibility of families of elliptic normal quintics and of rational nor mal quartics on a general cubic threefold is proved. This implies the uniqu eness of the moduli component under consideration. The techniques of Clemen s-Griffiths and Welters are used for the calculation of the infinitesimal A bel-Jacobi map.