Bitangents of tropical plane quartic curves

TL;DR

This paper investigates properties of smooth tropical plane quartic curves, revealing they have either infinitely many or exactly seven bitangent lines and are not hyperelliptic, highlighting parallels and differences with classical algebraic geometry.

Contribution

The paper establishes the number of bitangent lines for smooth tropical plane quartic curves and proves they cannot be hyperelliptic, extending classical geometric concepts into tropical geometry.

Findings

Every smooth tropical plane quartic has either infinitely many or exactly 7 bitangent lines.

A smooth tropical plane quartic cannot be hyperelliptic.

The properties of tropical quartics mirror and differ from classical algebraic quartics.

Abstract

We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either infinitely many or exactly 7 bitangent lines. We also prove that a smooth tropical plane quartic curve cannot be hyperelliptic.