  In this paper we study principally polarized complex abelian varieties that
admit an automorphism of order 3. It turns out that certain natural conditions
on the multiplicities of its action on the differentials of the first kind do
guarantee that those polarized varieties are not jacobians of curves. As an
application, we get another proof of the already known (thanks to Clemens and
Griffiths) fact that intermediate jacobians of certain cubic threefolds are not
jacobians of curves.
