A Tropical Count of Real Bitangents to Plane Quartic Curves
-
Published:2023-06-30
Issue:2
Volume:30
Page:
-
ISSN:1077-8926
-
Container-title:The Electronic Journal of Combinatorics
-
language:
-
Short-container-title:Electron. J. Combin.
Author:
Geiger Alheydis,Panizzut Marta
Abstract
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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics