Resumen de Slopes of trigonal fibred surfaces and of higher dimensional fibrations

Miguel Ángel Barja Yáñez , Lidia Stoppino

• We give lower bounds for the slope of higher dimensional fibrations f : X −→ B 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; this result in particular proves a conjecture due to Harris and Stankova-Frenkel.