Xiao's conjecture for general fibred surfaces
  We prove that the genus $g$, the relative irregularity $q_f$ and the Clifford index $c_f$ of a non-isotrivial fibration $f$ satisfy the inequality $q_f \leq g - c_f$. This gives in particular a proof of Xiao's conjecture for fibrations whose general fibres have maximal Clifford index. 
Miguel \'Angel Barja, V\'ictor Gonz\'alez-Alonso, Juan Carlos Naranjo
math.AG