A note on singularity indices of hyperelliptic fibrations

Cheng Gong; Zhiming Guo; Xin Lü

doi:10.1007/s00013-025-02198-8

A note on singularity indices of hyperelliptic fibrations

Cheng Gong
, Zhiming Guo^*
, Xin Lü

^*此作品的通讯作者

数学科学学院

Soochow University
East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

Let f:X→B be a relatively minimal hyperelliptic fibration of genus g. For such a fibration f, Xiao introduced a series of singularity indices si(f) for 2≤i≤g+2. These indices provide an effective way to study the geometry of f. It is known that si(f)≥0 for i≥3, but it is not clear whether s2(f) is non-negative. In this note, we construct a sequence of hyperelliptic fibrations with s2(f)<0, where the genus g can be arbitrarily large.

源语言	英语
页（从-至）	153-163
页数	11
期刊	Archiv der Mathematik
卷	126
期	2
DOI	https://doi.org/10.1007/s00013-025-02198-8
出版状态	已出版 - 2月 2026

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title = "A note on singularity indices of hyperelliptic fibrations",

abstract = "Let f:X→B be a relatively minimal hyperelliptic fibration of genus g. For such a fibration f, Xiao introduced a series of singularity indices si(f) for 2≤i≤g+2. These indices provide an effective way to study the geometry of f. It is known that si(f)≥0 for i≥3, but it is not clear whether s2(f) is non-negative. In this note, we construct a sequence of hyperelliptic fibrations with s2(f)<0, where the genus g can be arbitrarily large.",

keywords = "Degeneration, Hyperelliptic fibrations, Singularity indices, Surface fibrations",

author = "Cheng Gong and Zhiming Guo and Xin L{\"u}",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2025.",

year = "2026",

month = feb,

doi = "10.1007/s00013-025-02198-8",

language = "英语",

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T1 - A note on singularity indices of hyperelliptic fibrations

AU - Gong, Cheng

AU - Guo, Zhiming

AU - Lü, Xin

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2025.

PY - 2026/2

Y1 - 2026/2

N2 - Let f:X→B be a relatively minimal hyperelliptic fibration of genus g. For such a fibration f, Xiao introduced a series of singularity indices si(f) for 2≤i≤g+2. These indices provide an effective way to study the geometry of f. It is known that si(f)≥0 for i≥3, but it is not clear whether s2(f) is non-negative. In this note, we construct a sequence of hyperelliptic fibrations with s2(f)<0, where the genus g can be arbitrarily large.

AB - Let f:X→B be a relatively minimal hyperelliptic fibration of genus g. For such a fibration f, Xiao introduced a series of singularity indices si(f) for 2≤i≤g+2. These indices provide an effective way to study the geometry of f. It is known that si(f)≥0 for i≥3, but it is not clear whether s2(f) is non-negative. In this note, we construct a sequence of hyperelliptic fibrations with s2(f)<0, where the genus g can be arbitrarily large.

KW - Degeneration

KW - Hyperelliptic fibrations

KW - Singularity indices

KW - Surface fibrations

UR - https://www.scopus.com/pages/publications/105023529649

U2 - 10.1007/s00013-025-02198-8

DO - 10.1007/s00013-025-02198-8

M3 - 文章

AN - SCOPUS:105023529649

SN - 0003-889X

VL - 126

SP - 153

EP - 163

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 2

ER -

A note on singularity indices of hyperelliptic fibrations

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