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April, 2021 Extremal trigonal fibrations on rational surfaces
Cheng GONG, Shinya KITAGAWA, Jun LU
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J. Math. Soc. Japan 73(2): 505-524 (April, 2021). DOI: 10.2969/jmsj/82438243

Abstract

For a relatively minimal fibration $f : X \to \mathbb{P}^1$ of non-hyperelliptic curves of genus $g$, we know the Picard number $\rho(X) \leq 3g + 8$. We study the case where $\rho(X) = 3g + 8$ and the Mordell–Weil group of $f$ is trivial. Such an $f$ occurs only if $g \equiv 0$ or $1 \pmod{3}$, and we describe such $f : X \to \mathbb{P}^1$ explicitly.

Funding Statement

This work is supported by NSFC (No.11671140), NSFC-ISF (No.11761141005), Natural Science Foundation of Higher Education Institutions of Jiangsu Province, China (No.18KJB110026) and Science and Technology Commission of Shanghai Municipality (No.18dz2271000).

Citation

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Cheng GONG. Shinya KITAGAWA. Jun LU. "Extremal trigonal fibrations on rational surfaces." J. Math. Soc. Japan 73 (2) 505 - 524, April, 2021. https://doi.org/10.2969/jmsj/82438243

Information

Received: 12 April 2019; Revised: 17 November 2019; Published: April, 2021
First available in Project Euclid: 9 November 2020

Digital Object Identifier: 10.2969/jmsj/82438243

Subjects:
Primary: 14D06
Secondary: 14J26

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 2 • April, 2021
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