Xiao’s conjecture for general fibred surfaces

Abstract

Abstract We prove that the genus g, the relative irregularity q f q_{f} and the Clifford index c f c_{f} of a non-isotrivial fibration f satisfy the inequality q f ≤ g - c f q_{f}\leq g-c_{f} . This gives in particular a proof of Xiao’s conjecture for fibrations whose general fibres have maximal Clifford index.