On the Gonality of an Algebraic Curve and Its Abelian Automorphism Groups

Xin Lu; Sheng Li Tan

doi:10.1080/00927872.2013.865741

On the Gonality of an Algebraic Curve and Its Abelian Automorphism Groups

Xin Lu
, Sheng Li Tan^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

Let G be an abelian automorphism group of a complex algebraic curve of genus g ≥ 2 with gonality d, and let |G| be its order. We prove that (Formula presented.) except for the Fermat curve of degree d + 1, and (Formula presented.) if G is cyclic. Furthermore, if |G| > 2g − 2 + 2d and C admits a unique finite cover f: C → ℙ¹ of degree d, then f is a Galois cover.

源语言	英语
页（从-至）	1509-1523
页数	15
期刊	Communications in Algebra
卷	43
期	4
DOI	https://doi.org/10.1080/00927872.2013.865741
出版状态	已出版 - 3 4月 2015

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10.1080/00927872.2013.865741

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abstract = "Let G be an abelian automorphism group of a complex algebraic curve of genus g ≥ 2 with gonality d, and let |G| be its order. We prove that (Formula presented.) except for the Fermat curve of degree d + 1, and (Formula presented.) if G is cyclic. Furthermore, if |G| > 2g − 2 + 2d and C admits a unique finite cover f: C → ℙ1 of degree d, then f is a Galois cover.",

keywords = "Abelian automorphism group, Algebraic curve, Finite cover, Genus, Gonality",

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N2 - Let G be an abelian automorphism group of a complex algebraic curve of genus g ≥ 2 with gonality d, and let |G| be its order. We prove that (Formula presented.) except for the Fermat curve of degree d + 1, and (Formula presented.) if G is cyclic. Furthermore, if |G| > 2g − 2 + 2d and C admits a unique finite cover f: C → ℙ1 of degree d, then f is a Galois cover.

AB - Let G be an abelian automorphism group of a complex algebraic curve of genus g ≥ 2 with gonality d, and let |G| be its order. We prove that (Formula presented.) except for the Fermat curve of degree d + 1, and (Formula presented.) if G is cyclic. Furthermore, if |G| > 2g − 2 + 2d and C admits a unique finite cover f: C → ℙ1 of degree d, then f is a Galois cover.

KW - Abelian automorphism group

KW - Algebraic curve

KW - Finite cover

KW - Genus

KW - Gonality

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JO - Communications in Algebra

JF - Communications in Algebra

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ER -

On the Gonality of an Algebraic Curve and Its Abelian Automorphism Groups

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