A stratification of moduli of arbitrarily singular curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917331690586112 |
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| author | Bozlee, Sebastian Guevara, Christopher Smyth, David |
| author_facet | Bozlee, Sebastian Guevara, Christopher Smyth, David |
| contents | We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalized curves," closely related to the moduli space of all reduced, connected algebraic curves. We construct a stratification $\bigsqcup_Γ\mathscr{E}_Γ$ of $\mathscr{E}_{g,n}$ indexed by generalized dual graphs and prove that each stratum $\mathscr{E}_Γ$ is a fiber bundle over a finite quotient of a product of $\moduli_{g,n}$s. The fibers are moduli schemes parametrizing subalgebras of a fixed algebra, and are in principle explicitly computable as locally closed subschemes of products of Grassmannians. We thus obtain a remarkably explicit geometric description of moduli of reduced curves with arbitrary singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A stratification of moduli of arbitrarily singular curves Bozlee, Sebastian Guevara, Christopher Smyth, David Algebraic Geometry 14H10, 14H20 We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalized curves," closely related to the moduli space of all reduced, connected algebraic curves. We construct a stratification $\bigsqcup_Γ\mathscr{E}_Γ$ of $\mathscr{E}_{g,n}$ indexed by generalized dual graphs and prove that each stratum $\mathscr{E}_Γ$ is a fiber bundle over a finite quotient of a product of $\moduli_{g,n}$s. The fibers are moduli schemes parametrizing subalgebras of a fixed algebra, and are in principle explicitly computable as locally closed subschemes of products of Grassmannians. We thus obtain a remarkably explicit geometric description of moduli of reduced curves with arbitrary singularities. |
| title | A stratification of moduli of arbitrarily singular curves |
| topic | Algebraic Geometry 14H10, 14H20 |
| url | https://arxiv.org/abs/2307.10013 |