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Automorphism group of plane curve computed by Galois points. II. (English) Zbl 1396.14025

Summary: Recently, the first author [Proc. Japan Acad., Ser. A 94, No. 6, 59–63 (2018; Zbl 1396.14025)] classified finite groups obtained as automorphism groups of smooth plane curves of degree \(d\geq4\) into five types. He gave an upper bound of the order of the automorphism group for each types. For one of them, the type (a-ii), that is given by \(\max \{2d(d-2),60d\}\). In this article, we shall construct typical examples of smooth plane curve \(C\) by applying the method of Galois points, whose automorphism group has order \(60d\). In fact, we determine the structure of the automorphism group of those curves.
For part I, see [K. Miura and A. Ohbuchi, Beitr. Algebra Geom. 56, No. 2, 695–702 (2015; Zbl 1327.14145)].

MSC:

14H37 Automorphisms of curves
14H50 Plane and space curves
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References:

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