@article{Kamel2025, 
author = {Alwaleed Kamel and Eman Alluqmani and Mohammed A. Saleem and Waleed Khaled Elshareef},
title = {On classification of groups generated by total sextactic points of smooth quartic curves},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {28221-28242},
keywords = {sextactic points, algebraic curves, quartic curves, mutual conic, Jacobian, flex points, group theory},
url = {https://www.sciopen.com/article/10.3934/math.20251241},
doi = {10.3934/math.20251241},
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.}
}