On the automorphism group of non-singular plane curves fixing the degree

TL;DR

This paper investigates the automorphism groups of non-singular plane curves of degree d over algebraically closed fields of characteristic zero, building on Harui's previous results.

Contribution

It extends the understanding of automorphism groups for non-singular plane curves, addressing open questions following Harui's work.

Findings

Characterization of automorphism groups for specific degrees

Identification of conditions for automorphism group structures

Extension of Harui's results to broader classes of curves

Abstract

This note is devoted, after the result of Harui, arXiv:1306.5842, to solve some natural questions for non-singular plane curves of degree $d$ over an algebraically closed field $K$ of zero characteristic.