Xiao's conjecture for general fibred surfaces

2014/01/29 by Miguel Ángel Barja, Barja, Miguel Ángel, Víctor González‐Alonso +3
Mathematics · #14D06 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1401.7502

openalex publication_date 2014/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• On the slope of hyperelliptic fibrations with positive relative irregularity

Related

• Xiao's Conjecture on Canonically Fibered Surfaces
• Trigonal Canonically Fibered Surfaces
• On the slope conjecture of Barja and Stoppino for fibred surfaces
• A Note on a Conjecture of Xiao
• Maximally irregularly fibred surfaces of general type