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^*

^*Corresponding author for this work

School of Mathematical Sciences

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

2 Scopus citations

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.

Original language	English
Pages (from-to)	1509-1523
Number of pages	15
Journal	Communications in Algebra
Volume	43
Issue number	4
DOIs	https://doi.org/10.1080/00927872.2013.865741
State	Published - 3 Apr 2015

Keywords

Abelian automorphism group
Algebraic curve
Finite cover
Genus
Gonality

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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.",

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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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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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Keywords

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