Plane quartics and heptagons
Algebraic Geometry
2024-08-29 v1
Abstract
Every polygon with n vertices in the complex projective plane is naturally associated with its adjoint curve of degree n-3. Hence the adjoint of a heptagon is a plane quartic. We prove that a general plane quartic is the adjoint of exactly 864 distinct complex heptagons. This number had been numerically computed by Kohn et al. We use intersection theory and the Scorza correspondence for quartics to show that 864 is an upper bound, complemented by a lower bound obtained through explicit analysis of the famous Klein quartic.
Cite
@article{arxiv.2408.15759,
title = {Plane quartics and heptagons},
author = {Daniele Agostini and Daniel Plaumann and Rainer Sinn and Jannik Lennart Wesner},
journal= {arXiv preprint arXiv:2408.15759},
year = {2024}
}
Comments
18 pages, 1 figure