A proof of a conjecture by Monin and Rana on equations defining $\bar{M}_{0,n}$

TL;DR

This paper proves a conjecture by Monin and Rana that describes the equations defining the moduli space ar{M}_{0,n} in a specific embedding, confirming the conjecture for all n, extending previous computational verifications.

Contribution

The paper provides a general proof of Monin and Rana's conjecture for all n, establishing the defining equations of ar{M}_{0,n} in the given embedding.

Findings

Confirmed the conjecture for all n.

Derived explicit equations for ar{M}_{0,n}.

Extended previous computational results to a general proof.

Abstract

Monin and Rana conjectured a set of equations defining the image of the moduli space $\bar{M}_{0,n}$ under an embedding into $\mathbb{P}^1\times \cdots\times \mathbb{P}^{n-3}$ due to Keel and Tevelev and verified the conjecture for $n\leq 8$ using Macaulay2. We prove this conjecture for all $n$.