A smooth tropical plane 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 Plücker and Zeuthen's count of the number of real bitangents to smooth plane quartic curves.
@article{10_37236_11099,
author = {Alheydis Geiger and Marta Panizzut},
title = {A tropical count of real bitangents to plane quartic curves},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11099},
zbl = {1539.14135},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11099/}
}
TY - JOUR
AU - Alheydis Geiger
AU - Marta Panizzut
TI - A tropical count of real bitangents to plane quartic curves
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11099/
DO - 10.37236/11099
ID - 10_37236_11099
ER -
%0 Journal Article
%A Alheydis Geiger
%A Marta Panizzut
%T A tropical count of real bitangents to plane quartic curves
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11099/
%R 10.37236/11099
%F 10_37236_11099
Alheydis Geiger; Marta Panizzut. A tropical count of real bitangents to plane quartic curves. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11099
