Slope inequalities for higher dimensional irregular fibrations

We prove the equivalence between Clifford-Severi inequalities for good classes of varieties of maximal Albanese dimension and Slope Inequalities for such varieties fibred over curves. This provides a big set of new Slope Inequalities and characterizes the limit cases. It also gives a machinery to automatically obtain other higher dimensional Slope and CliffordSeveri inequalities from inequalities in low dimension. For this, we construct a continuous version of Xiao’s method for irregular fibrations.