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

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	505-524
Number of pages	20
Journal	Journal of the Mathematical Society of Japan
Volume	73
Issue number	2
DOIs	https://doi.org/10.2969/JMSJ/82438243
State	Published - Apr 2021

Keywords

Mordell-Weil groups
Rational surfaces
Trigonal fibrations

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10.2969/JMSJ/82438243

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title = "Extremal trigonal fibrations on rational surfaces",

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.",

keywords = "Mordell-Weil groups, Rational surfaces, Trigonal fibrations",

author = "Cheng Gong and Shinya Kitagawa and Jun Lu",

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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

UR - https://www.scopus.com/pages/publications/85105931730

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DO - 10.2969/JMSJ/82438243

M3 - 文章

AN - SCOPUS:85105931730

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JO - Journal of the Mathematical Society of Japan

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IS - 2

ER -

Extremal trigonal fibrations on rational surfaces

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Keywords

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