Theorem of Martens on symmetric products of curves (following Ziv Ran)

We wil prove that any birational map between the $d$-th symmetric products of nonsingular curves over field of characteristic 0 is induced by a birational map between curves themselves, provided $d \leq g-2$. It can be considered an extension of curve Torelli theorem claiming a little less for $d=g-1$ (for further degrees this proposition goes awry).