Abstract

A Jacobian variety that is isogenous to a product of elliptic curves is called a completely decomposable Jacobian. They have been widely studied but there still remain some key questions unsolved. For instance, it is still unknown if there is a completely decomposable Jacobian on each dimension. In this work we study and completely characterize the families of curves with the action of a symmetric group, such that the group algebra decomposition for the corresponding Jacobian is a product of elliptic curves.