# Simplicial equations for the moduli space of stable rational curves

## TL;DR

This paper demonstrates how the combinatorial simplicial structure of moduli spaces of stable rational curves enables explicit equation derivation, using elementary tree combinatorics.

## Contribution

It introduces a method to produce explicit equations for moduli spaces based on their simplicial structure and combinatorial properties.

## Key findings

- Explicit equations for moduli spaces derived from simplicial structures
- Elementary combinatorial arguments about trees underpin the equations
- Provides a framework for understanding the algebraic structure of these moduli spaces

## Abstract

In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial statement about the sets of trees with marked leaves.