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Xiao’s conjecture for general fibred surfaces. (English) Zbl 1437.14020

Summary: 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.

MSC:

14D06 Fibrations, degenerations in algebraic geometry
14J29 Surfaces of general type
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