Algebra of global sections of ψ-bundles on M0,n

Polishchuk, Alexander; Rains, Eric

doi:10.2140/ant.2026.20.1841

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Algebra of global sections of $\psi$-bundles on ${}\mkern4mu\overline{\mkern-4mu M\mkern-1mu}\mkern1mu{} _{0,n}$

Alexander Polishchuk and Eric Rains

Vol. 20 (2026), No. 9, 1841–1854

DOI: 10.2140/ant.2026.20.1841

Abstract

We consider the $ℤ^{n}$ -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 ${\bar{M}}_{0, n} [ψ]$ of $ψ$ -stable curves of genus $0$ is Cohen–Macaulay and normal, and the natural map ${\bar{M}}_{0, n} \to {\bar{M}}_{0, n} [ψ]$ is a rational resolution.

Keywords

moduli space of curves, Cohen–Macaulay singularity, $\psi$-stable curves

Mathematical Subject Classification

Primary: 14H10

Milestones

Received: 15 August 2024

Revised: 6 June 2025

Accepted: 5 August 2025

Published: 19 October 2026

Authors

Alexander Polishchuk
Department of Mathematics University of Oregon Eugene, OR United States	National Research University Higher School of Economics Moscow Russia

Eric Rains
Department of Mathematics California Institute of Technology Pasadena, CA United States

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Vol. 20, No. 9, 2026