# Higher balancing for locally tropically convex tropical varieties

## TL;DR

This paper demonstrates that locally tropically convex tropical varieties possess a canonical polyhedral structure satisfying higher balancing conditions at all cells of positive codimension, enhancing understanding of their geometric properties.

## Contribution

It introduces the concept of higher balancing conditions for locally tropically convex tropical varieties, providing a new structural insight.

## Key findings

- Existence of a canonical polyhedral structure for these varieties
- Higher balancing conditions hold at all cells of positive codimension
- Advances understanding of tropical geometric structures

## Abstract

In this text, we show that locally tropically convex tropical varieties in $\mathbb{R}^n$ have locally a canonical polyhedral structure that satisfies higher balancing conditions at all cells of positive codimension.