Automorphism groups of smooth plane curves

2013/06/25 by Takeshi Harui, Harui, Takeshi · 3 citations
Mathematics · #14H37 #14H50 #20G20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1306.5842

openalex publication_date 2013/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with large automorphism groups. This paper also contains a simple proof of the uniqueness of smooth plane curves with the full automorphism group of maximal order for each degree.

Cited by

• Large orders of automorphisms of smooth curves in \mathbb P¹× \mathbb P¹
• Automorphism groups of smooth cubic threefolds
• Automorphism group of plane curve computed by Galois points, II

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