Abstract:
We will explain various higher dimensional generalizations of the Xiao-Cornalba-Harris slope inequality, and we will present several effective positivity results for Hodge bundles. We will talk about applications regarding the volume of integrable foliations, the volume and the ample cone of KSB moduli spaces, and the cardinality of the auotmorphism group of KSB fibrations.
This is based on joint works with Zs. Patakfalvi, L. Tasin, F. Viviani.