Higher dimensional slope inequalities [1]

Abstract. Consider a family of varieties f: X-> T, where T is a curve.  We prove several inequalities about the slope of f, which are generalisations of Xiao and Cornalba-Harris inequalities in the case where X is a surface.  We then apply our results to the KSB moduli space of stable varieties to study the ample cone of such spaces. 

The talk is based on a joint work with Giulio Codogni and Filippo Viviani.