# Xiao’s conjecture for general fibred surfaces

Xiao’s conjecture for general fibred surfaces AbstractWe prove that the genus g, the relative irregularity qfq_{f}and the Clifford index cfc_{f}of a non-isotrivial fibration f satisfy the inequality qf≤g-cfq_{f}\leq g-c_{f}. This gives in particular a proof of Xiao’s conjecture for fibrations whose general fibres have maximal Clifford index. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal für die reine und angewandte Mathematik de Gruyter

# Xiao’s conjecture for general fibred surfaces

, Volume 2018 (739): 12 – Jun 1, 2018
12 pages

/lp/degruyter/xiao-s-conjecture-for-general-fibred-surfaces-VBV4jf87pL
Publisher
De Gruyter
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1435-5345
eISSN
1435-5345
D.O.I.
10.1515/crelle-2015-0080
Publisher site
See Article on Publisher Site

### Abstract

AbstractWe prove that the genus g, the relative irregularity qfq_{f}and the Clifford index cfc_{f}of a non-isotrivial fibration f satisfy the inequality qf≤g-cfq_{f}\leq g-c_{f}. This gives in particular a proof of Xiao’s conjecture for fibrations whose general fibres have maximal Clifford index.

### Journal

Journal für die reine und angewandte Mathematikde Gruyter

Published: Jun 1, 2018

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