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Research Article | Open Access

On classification of groups generated by total sextactic points of smooth quartic curves

Alwaleed Kamel1,2, Eman Alluqmani3, Mohammed A. Saleem2, Waleed Khaled Elshareef2,4( )
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia
Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82749, Egypt
Department of Mathematics, Faculty of Science, Umm Al-Qura University, P.O. Box 14035, Makkah, 21955, Saudi Arabia
Faculty of Computers and Information Technology, EELU, Giza Governorate, 12611, Egypt
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Abstract

We introduced a new concept, the mutual conic, in order to give a complete classification of the group G generated by the images of two or three total sextactic points in the Jacobian J C of a smooth projective plane quartic curve C (3-genus curves that are non-hyperelliptic), and we determined the geometric configuration of these points associated with each case. We supported the validity of the results with a variety of examples.

Keywords

sextactic pointsalgebraic curvesquartic curvesmutual conicJacobianflex pointsgroup theory
CLC number: 11G30, 14H45, 20F05

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 28221-28242
DOI: 10.3934/math.20251241

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Cite this article:
Kamel A, Alluqmani E, Saleem MA, et al. On classification of groups generated by total sextactic points of smooth quartic curves. AIMS Mathematics, 2025, 10(12): 28221-28242. https://doi.org/10.3934/math.20251241

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Received: 04 July 2025
Revised: 29 October 2025
Accepted: 11 November 2025
Published: 01 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)