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Journal für die reine und angewandte Mathematik

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Volume 2018, Issue 739


Xiao’s conjecture for general fibred surfaces

Miguel Ángel Barja
  • Departament de Matemàtiques, Universitat Politècnica de Catalunya (UPC-BarcelonaTECH), Av. Diagonal 647, 08028 Barcelona, Spain
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/ Víctor González-Alonso / Juan Carlos Naranjo
  • Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
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Published Online: 2016-01-14 | DOI: https://doi.org/10.1515/crelle-2015-0080


We prove that the genus g, the relative irregularity qf and the Clifford index cf of a non-isotrivial fibration f satisfy the inequality qfg-cf. This gives in particular a proof of Xiao’s conjecture for fibrations whose general fibres have maximal Clifford index.


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About the article

Received: 2015-03-18

Revised: 2015-07-07

Published Online: 2016-01-14

Published in Print: 2018-06-01

Funding Source: Ministerio de Economía y Competitividad

Award identifier / Grant number: MTM2012-38122-C03-01/FEDER

Award identifier / Grant number: MTM2012-38122-C03-02

Funding Source: Generalitat de Catalunya

Award identifier / Grant number: 2009-SGR-1284

Funding Source: H2020 European Research Council

Award identifier / Grant number: StG 279723 ‘Arithmetic of algebraic surfaces’ (SURFARI)

During the development of this work, the first and second authors were supported by the Spanish ‘Ministerio de Economía y Competitividad’ (project MTM2012-38122-C03-01/FEDER) and the ‘Generalitat de Catalunya’ (project 2009-SGR-1284). The third author was supported by the Spanish ‘Ministerio de Economía y Competitividad’ (project MTM2012-38122-C03-02). The second author was also supported by the Spanish ‘Ministerio de Educación’ (grant FPU-AP2008-01849) and by the ‘European Research Council’ (StG 279723 ‘Arithmetic of algebraic surfaces’, SURFARI).

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 739, Pages 297–308, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0080.

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