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arXiv · 2405.21062

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

Alexander Polishchuk·Eric Rains
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Abstract

We consider the ${\mathbb Z}^n$-graded algebra of global sections of line bundles generated by the standard line bundles $L_1,\ldots,L_n$ 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.

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Alexander Polishchuk, Eric Rains. 2024-05-31. Algebra of global sections of $\psi$-bundles on $\bar{M}_{0,n}$. https://arxiv.org/abs/2405.21062

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