Xiao's conjecture for general fibred surfaces

Miguel Ángel Barja; Víctor González-Alonso; Juan Carlos Naranjo

Xiao's conjecture for general fibred surfaces

Algebraic Geometry 2015-07-08 v4

Authors: Miguel Ángel Barja , Víctor González-Alonso , Juan Carlos Naranjo

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

Keywords

fibrations

Cite

@article{arxiv.1401.7502,
  title  = {Xiao's conjecture for general fibred surfaces},
  author = {Miguel Ángel Barja and Víctor González-Alonso and Juan Carlos Naranjo},
  journal= {arXiv preprint arXiv:1401.7502},
  year   = {2015}
}

Comments

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

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