Xiao's conjecture for general fibred surfaces

Abstract

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 $q_f\le g-c_f$. This gives in particular a proof of Xiao's conjecture for fibrations whose general fibres have maximal Clifford index.

Exposition changed and new references added, thanks to comments of the referees

References in corpus (2)

• Dihedral Monodromy and Xiao Fibrations
• On the slope of hyperelliptic fibrations with positive relative irregularity

Cited by in corpus (2)

• On deformations of curves supported on rigid divisors
• On the rank of the flat unitary summand of the Hodge bundle