Sharp Bound on Abelian Automorphism Groups of Surfaces of General Type

Xin Lü; Sheng Li Tan

doi:10.1090/memo/1576

Sharp Bound on Abelian Automorphism Groups of Surfaces of General Type

School of Mathematical Sciences

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

Abstract

We prove that the order of an abelian (resp. cyclic) automorphism group of a minimal complex projective surface S of general type is bounded from above by 12.5K_S² + 100 (resp. 12.5K_S² + 90) provided that the geometric genus of the surface is greater than 6. The upper bounds are both reached for infinitely many surfaces whose geometric genera can be arbitrarily large.

Original language	English
Journal	Memoirs of the American Mathematical Society
Volume	311
Issue number	1576
DOIs	https://doi.org/10.1090/memo/1576
State	Published - Jul 2025

Keywords

Abelian automorphism
fibration
surface of general type

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10.1090/memo/1576

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title = "Sharp Bound on Abelian Automorphism Groups of Surfaces of General Type",

abstract = "We prove that the order of an abelian (resp. cyclic) automorphism group of a minimal complex projective surface S of general type is bounded from above by 12.5KS2 + 100 (resp. 12.5KS2 + 90) provided that the geometric genus of the surface is greater than 6. The upper bounds are both reached for infinitely many surfaces whose geometric genera can be arbitrarily large.",

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author = "Xin L{\"u} and Tan, \{Sheng Li\}",

year = "2025",

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doi = "10.1090/memo/1576",

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T1 - Sharp Bound on Abelian Automorphism Groups of Surfaces of General Type

AU - Lü, Xin

AU - Tan, Sheng Li

PY - 2025/7

Y1 - 2025/7

N2 - We prove that the order of an abelian (resp. cyclic) automorphism group of a minimal complex projective surface S of general type is bounded from above by 12.5KS2 + 100 (resp. 12.5KS2 + 90) provided that the geometric genus of the surface is greater than 6. The upper bounds are both reached for infinitely many surfaces whose geometric genera can be arbitrarily large.

AB - We prove that the order of an abelian (resp. cyclic) automorphism group of a minimal complex projective surface S of general type is bounded from above by 12.5KS2 + 100 (resp. 12.5KS2 + 90) provided that the geometric genus of the surface is greater than 6. The upper bounds are both reached for infinitely many surfaces whose geometric genera can be arbitrarily large.

KW - Abelian automorphism

KW - fibration

KW - surface of general type

UR - https://www.scopus.com/pages/publications/105022741216

U2 - 10.1090/memo/1576

DO - 10.1090/memo/1576

M3 - 文章

AN - SCOPUS:105022741216

SN - 0065-9266

VL - 311

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

IS - 1576

ER -

Sharp Bound on Abelian Automorphism Groups of Surfaces of General Type

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