Algebra of global sections of $\psi$-bundles on ${\bar{M}}_{0,n}$

Abstract

We consider the ${\mathbb{Z}}^n$-graded algebra of global sections of line bundles generated by the standard line bundles $L_1,\dots ,L_n$ on ${\bar{M}}_{0,n}$. We find a simple presentation of this algebra by generators and quadratic relations. As an application we prove that the moduli space ${\bar{M}}_{0,n}[\psi ]$ of $\psi$-stable curves of genus $0$ is Cohen-Macaulay and normal, and the natural map ${\bar{M}}_{0,n}\to {\bar{M}}_{0,n}[\psi ]$ is a rational resolution.

10 pages