Algebra of global sections of ψ-bundles on M̄0,n

We consider the Zⁿ-graded algebra of global sections of line bundles generated by the standard line bundles L₁,…,Lₙ on M̄0,n. We find a simple presentation of this algebra by generators and quadratic relations. As an application we prove that the moduli space M̄0,n[ψ] of ψ-stable curves of genus $0$ is Cohen-Macaulay and normal, and the natural map M̄0,n→ M̄0,n[ψ] is a rational resolution.