Tropical limit of log-inflection points for planar curves

TL;DR

This paper investigates the behavior of log-inflection points of complex planar curves as they approach their tropical limits, revealing that these points tend to accumulate in pairs at midpoints of bounded edges in the tropical curve.

Contribution

It introduces a detailed analysis of how log-inflection points behave in the tropical limit, highlighting their pairing and accumulation at specific locations.

Findings

Log-inflection points accumulate in pairs at midpoints of bounded edges.

The behavior of log-inflection points is characterized in the tropical limit.

The study connects complex curve inflection points with tropical geometry structures.

Abstract

The paper describes behavior of log-inflection points of curves in $(\mathbb{C}^*)^2$ under passing to the tropical limit. We show that such points accumulate by pairs at the midpoints of bounded edges in the limiting tropical curve. Log-inflection points are points of inflection with respect to the parallelization of $(\mathbb{C}^*)^2$ given by the multiplicative group law.