On the slope of hyperelliptic fibrations with positive relative irregularity

2013/11/28 by Xin Lü, Kang Zuo, Lu, Xin +1 · 2 citations
Computer Science · Mathematics · #14D06 #14D99 #14H10 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1311.7271

openalex publication_date 2013/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f: S → B be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus g≥ 2 with relative irregularity q_f. We show a sharp lower bound on the slope λ_f of f. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of λ_f as an increasing function of q_f in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if λ_f<4.

Cited by

• On the slope conjecture of Barja and Stoppino for fibred surfaces
• Xiao's conjecture for general fibred surfaces

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