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Automorphism groups and signatures of smooth septic curves

Part of: Curves

Published online by Cambridge University Press:  13 May 2025

E. Badr Open the ORCID record for E. Badr [Opens in a new window] ,
A. El-Guindy Open the ORCID record for A. El-Guindy [Opens in a new window]  and
M. Kamel Open the ORCID record for M. Kamel [Opens in a new window]
E. Badr
Affiliation:
Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt Mathematics and Actuarial Science Department, American University in Cairo, New Cairo, Egypt
A. El-Guindy
Affiliation:
Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt
M. Kamel*
Affiliation:
Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt
*
Corresponding author: M. Kamel; Email: mohgamal@sci.cu.edu.eg
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Abstract

We determine the list of automorphism groups for smooth plane septic curves over an algebraically closed field $K$ of characteristic $0$, as well as their signatures. For each group, we also provide a geometrically complete family over $K$, which consists of a generic defining polynomial equation describing each locus up to $K$-projective equivalence. Notably, we present two distinct examples of what we refer to as final strata of smooth plane curves.

Keywords

Plane curvesautomorphism groupssignature

MSC classification

Primary: 14H37: Automorphisms 14H10: Families, moduli (algebraic) 14H45: Special curves and curves of low genus 14H50: Plane and space curves

Information

Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

Dedicated to the memory of our teacher and mentor Professor Nabil L. Youssef

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