Note on smoothness condition on tropical elliptic curves of symmetric truncated cubic forms

TL;DR

This paper establishes explicit coefficient conditions for smoothness in tropical elliptic curves derived from symmetric truncated cubic forms and explores cases where the curves are non-smooth based on subdivision types.

Contribution

It provides explicit smoothness criteria for symmetric truncated cubic tropical curves and analyzes non-smooth cases related to specific subdivisions.

Findings

Explicit coefficient conditions for smooth tropical elliptic curves.

Identification of subdivision types leading to non-smooth curves.

Analysis of non-smooth cases in relation to specific subdivisions.

Abstract

In this work, we provide explicit conditions for the coefficients of a symmetric truncated cubic to give a smooth tropical curve. We also examine non-smooth cases corresponding to some specific subdivision types.