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

Xiao’s conjecture for general fibred surfaces