A stratification of moduli of arbitrarily singular curves
| Autor: | Bozlee, Sebastian, Guevara, Christopher, Smyth, David |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalized curves" which is a minor modification of the moduli space of all reduced, connected curves. We construct a stratification $\bigsqcup_\Gamma \mathscr{E}_\Gamma$ of $\mathscr{E}_{g,n}$ indexed by generalized dual graphs and prove that each stratum $\mathscr{E}_{\Gamma}$ is a fiber bundle over a finite quotient of a product of $\mathcal{M}_{g,n}$'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. Comment: Rewritten introduction, correction in Theorem 6.34. 45 pages, comments welcome! |
| Databáze: | arXiv |
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