A tropical count of real bitangents to plane quartic curves
Algebraic Geometry
2021-12-09 v1 Combinatorics
Abstract
A smooth tropical quartic curve has seven tropical bitangent classes. Their shapes can vary within the same combinatorial type of curve. We study deformations of these shapes and we show that the conditions determined by Cueto and Markwig for lifting them to real bitangent lines are independent of the deformations. From this we deduce a tropical proof of Pl\"{u}cker and Zeuthen's count of the number of real bitangents to smooth plane quartic curves.
Keywords
Cite
@article{arxiv.2112.04433,
title = {A tropical count of real bitangents to plane quartic curves},
author = {Alheydis Geiger and Marta Panizzut},
journal= {arXiv preprint arXiv:2112.04433},
year = {2021}
}
Comments
29 pages, various figures