Tan's conjecture on irregular family over P1

Xin Lü; Peng Sun

doi:10.1016/j.jalgebra.2025.12.005

Tan's conjecture on irregular family over P¹

Xin Lü
, Peng Sun^*

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

Let f:S→P¹ be a non-trivial semi-stable fibration of genus g≥2 with s singular fibers over the complex numbers. Tan conjectured that s≥6 if g≫0. We study this conjecture for irregular surfaces. More precisely, we prove that s≥6 if the irregularity q(S)≥2.

Original language	English
Pages (from-to)	488-503
Number of pages	16
Journal	Journal of Algebra
Volume	691
DOIs	https://doi.org/10.1016/j.jalgebra.2025.12.005
State	Published - 1 Apr 2026

Keywords

Fibration
Irregular surface
Singular fiber

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10.1016/j.jalgebra.2025.12.005

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title = "Tan's conjecture on irregular family over P1",

abstract = "Let f:S→P1 be a non-trivial semi-stable fibration of genus g≥2 with s singular fibers over the complex numbers. Tan conjectured that s≥6 if g≫0. We study this conjecture for irregular surfaces. More precisely, we prove that s≥6 if the irregularity q(S)≥2.",

keywords = "Fibration, Irregular surface, Singular fiber",

author = "Xin L{\"u} and Peng Sun",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2026",

month = apr,

day = "1",

doi = "10.1016/j.jalgebra.2025.12.005",

language = "英语",

volume = "691",

pages = "488--503",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Tan's conjecture on irregular family over P1

AU - Lü, Xin

AU - Sun, Peng

PY - 2026/4/1

Y1 - 2026/4/1

N2 - Let f:S→P1 be a non-trivial semi-stable fibration of genus g≥2 with s singular fibers over the complex numbers. Tan conjectured that s≥6 if g≫0. We study this conjecture for irregular surfaces. More precisely, we prove that s≥6 if the irregularity q(S)≥2.

AB - Let f:S→P1 be a non-trivial semi-stable fibration of genus g≥2 with s singular fibers over the complex numbers. Tan conjectured that s≥6 if g≫0. We study this conjecture for irregular surfaces. More precisely, we prove that s≥6 if the irregularity q(S)≥2.

KW - Fibration

KW - Irregular surface

KW - Singular fiber

UR - https://www.scopus.com/pages/publications/105024189189

U2 - 10.1016/j.jalgebra.2025.12.005

DO - 10.1016/j.jalgebra.2025.12.005

M3 - 文章

AN - SCOPUS:105024189189

SN - 0021-8693

VL - 691

SP - 488

EP - 503

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Tan's conjecture on irregular family over P¹

Abstract

Keywords

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