Miguel Ángel Barja (Universitat Politècnica de Catalunya)

From slopes of fibred surfaces to continuous rank functions and Clifford-Severi inequalities for irregular varieties

Abstract

In recent years Pardini, Stoppino and myself have introduced new techniques in order to study irregular varieties, the so called continuous rank functions and the eventual maps. I will explain how they allow to obtain geographic results on such varieties, as the Clifford-Severi inequalities, and why the cases of curves and surfaces are the key ones in order to obtain results in higher dimension by an induction process. I will also show how these techniques originated in the classical work of Xiao and Konno of the study of the slopes of fibred surfaces.