  We study the Fourier-Mukai functor D(Y) -> D(X) induced by the universal
family on a fine moduli space Y for simple semihomogeneous vector bundles on an
abelian variety X. The main result is that the Fourier-Mukai transform of a
very negative line bundle on Y is ample if and only if the bundles parametrized
by Y are nef.

Algebraic Geometry