Galois covers of the projective line by smooth plane curves of large degree

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry - Tập 64 - Trang 311-365 - 2022
Taro Hayashi1
1Faculty of Agriculture, Kindai University, Nara, Japan

Tóm tắt

Let C be an irreducible plane curve of degree $$d\ge 4$$ . A point $$p\in {\mathbb {P}}^1$$ is called a Galois point of C if the projection $$\pi _p:C\rightarrow {\mathbb {P}}^1$$ at p is a Galois cover. In this paper, based on the Galois point of plane curves, we will study Galois covers of the projective line whose covering spaces are smooth plane curves. Let G be a subgroup of the automorphism group of C. Under the assumption that the degree of C is 121 or more, we will give necessary and sufficient conditions for G to be $$C/G\cong {\mathbb {P}}^1$$ .

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Thông tin xuất bản

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Tập 64

311-365

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