Extremal trigonal fibrations on rational surfaces

Cheng Gong; Shinya Kitagawa; Jun Lu

doi:10.2969/JMSJ/82438243

Extremal trigonal fibrations on rational surfaces

Cheng Gong
, Shinya Kitagawa
, Jun Lu

数学科学学院

Soochow University
National Institute of Technology, Gifu College

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

For a relatively minimal fibration f : X → P¹ of non-hyperelliptic curves of genus g, we know the Picard number ρ(X) ≤ 3g + 8. We study the case where ρ(X) = 3g + 8 and the Mordell-Weil group of f is trivial. Such an f occurs only if g ≡ 0 or 1 (mod 3), and we describe such f : X → P¹ explicitly.

源语言	英语
页（从-至）	505-524
页数	20
期刊	Journal of the Mathematical Society of Japan
卷	73
期	2
DOI	https://doi.org/10.2969/JMSJ/82438243
出版状态	已出版 - 4月 2021

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abstract = "For a relatively minimal fibration f : X → P1 of non-hyperelliptic curves of genus g, we know the Picard number ρ(X) ≤ 3g + 8. We study the case where ρ(X) = 3g + 8 and the Mordell-Weil group of f is trivial. Such an f occurs only if g ≡ 0 or 1 (mod 3), and we describe such f : X → P1 explicitly.",

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AB - For a relatively minimal fibration f : X → P1 of non-hyperelliptic curves of genus g, we know the Picard number ρ(X) ≤ 3g + 8. We study the case where ρ(X) = 3g + 8 and the Mordell-Weil group of f is trivial. Such an f occurs only if g ≡ 0 or 1 (mod 3), and we describe such f : X → P1 explicitly.

KW - Mordell-Weil groups

KW - Rational surfaces

KW - Trigonal fibrations

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Extremal trigonal fibrations on rational surfaces

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