# Connectedness of the Moduli Space of Genus 1 Planar Tropical Curves

## TL;DR

This paper proves that the moduli space of genus one planar tropical curves with arbitrary degree and marked edges is connected, advancing understanding in tropical geometry and its relation to algebraic geometry.

## Contribution

It establishes the connectedness of the moduli space of genus one planar tropical curves, a new result in tropical geometry.

## Key findings

- Moduli spaces of genus one planar tropical curves are connected.
- Defined properties and types of tropical curves including combinatorial and degree aspects.
- Analyzed the structure of the moduli space for arbitrary degree and marked edges.

## Abstract

Tropical geometry is a relatively recent field in mathematics created as a simplified model for certain problems in algebraic geometry. We introduce the definition of abstract and planar tropical curves as well as their properties, including combinatorial type and degree. We also talk about the moduli space, a geometric object that parameterizes all possible types of abstract or planar tropical curves subject to certain conditions. Our research focuses on the moduli spaces of planar tropical curves of genus one, arbitrary degree d and any number of marked, unbounded edges. We prove that these moduli spaces are connected.