  We give lower bounds for the slope of higher dimensional fibrations over
curves under conditions of GIT-semistability of the fibres, using a
generalization of a method of Cornalba and Harris. With the same method we
establish a sharp lower bound for the slope of trigonal fibrations of even
genus and general Maroni invariant; in particular this result proves a
conjecture due to Harris and Stankova-Frenkel.
