Relative Jacobians of elliptic fibrations with reducible fibers

We prove that if X and S   are smooth varieties and f:X→Sf:X→S is an elliptic fibration with singular fibers curves of types IN with N≥1N≥1, II, III and IV, then the relative Jacobian fˆ:M¯X/S→S of f, defined as the relative moduli space of semistable pure dimension one sheaves of rank 1 and degree 0 on the fibers of f, is an elliptic fibration such that all its fibers are irreducible. This extends known results when fibers are integral or of type I2.