Bitangents of non-smooth tropical quartics

TL;DR

This paper investigates the properties of bitangent lines to non-smooth tropical quartic curves, establishing their count and behavior under deformations, which advances understanding in tropical geometry.

Contribution

It proves that non-smooth tropical quartics have exactly 7 classes of bitangent lines with multiplicities, and shows these multiplicities vary continuously in families.

Findings

Every non-smooth tropical quartic has 7 equivalence classes of bitangent lines.

Bitangent line multiplicities vary continuously in families of tropical curves.

The study extends classical results to the non-smooth tropical setting.

Abstract

We study bitangents of non-smooth tropical plane quartics. Our main result is that with appropriate multiplicities, every such curve has 7 equivalence classes of bitangent lines. Moreover, the multiplicity of bitangent lines varies continuously in families of tropical plane curves.