Algebra of global sections of $ψ$-bundles on $\bar{M}_{0,n}$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913371905851392 |
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| author | Polishchuk, Alexander Rains, Eric |
| author_facet | Polishchuk, Alexander Rains, Eric |
| contents | 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 $\bar{M}_{0,n}[ψ]$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_21062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebra of global sections of $ψ$-bundles on $\bar{M}_{0,n}$ Polishchuk, Alexander Rains, Eric Algebraic Geometry 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 $\bar{M}_{0,n}[ψ]$ 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. |
| title | Algebra of global sections of $ψ$-bundles on $\bar{M}_{0,n}$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.21062 |