On the irreducible components of the compactified Jacobian of a ribbon

In this article, we study the irreducible components of the compactified Jacobian of a ribbon X of arithmetic genus g over a smooth curve of genus . We prove that when the moduli space of rank 2 semistable vector bundles over is not an irreducible component and we determine the irreducible components in which it is contained. This answers a question of Chen and Kass in Ref. [2] and completes their results.