Effective cone of $overline{M}_{0,n}$ for odd $n$

TL;DR

This paper computes the effective cone of the moduli space of genus 0 curves with n marked points for odd n, using the equivalence with weighted point configurations on the projective line.

Contribution

It provides the first explicit computation of the effective cone for $ar{M}_{0,n}$ when n is odd, leveraging the space of stable weighted point configurations.

Findings

Effective cone computed for odd n

Utilizes equivalence with weighted point configurations

Advances understanding of $ar{M}_{0,n}$ geometry

Abstract

In this work, we compute the effective cone of the space of $n$ pointed genus 0 rational curves, $\bar{M}_{0,n}$ for odd $n$. We will, in fact, use the equivalence of $\bar{M}_{0,n}$ and the space of (semi) stable configurations of $n$ weighted points on $\mathbb{CP}^{1}$ with special weight $(1,..., 1)$ up to symmetric group action.