Abstract
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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Hayashi, T. Galois covers of the projective line by smooth plane curves of large degree. Beitr Algebra Geom 64, 311–365 (2023). https://doi.org/10.1007/s13366-022-00635-1
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DOI: https://doi.org/10.1007/s13366-022-00635-1