A stratification of moduli of arbitrarily singular curves

Sebastian Bozlee; Christopher Guevara; David Smyth

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arXiv · 2307.10013

A stratification of moduli of arbitrarily singular curves

Sebastian Bozlee·Christopher Guevara·David Smyth

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Abstract

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 $\bigsqcup_\Gamma \mathscr{E}_\Gamma$ 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 $\moduli_{g,n}$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.

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BibTeX RIS

Sebastian Bozlee, Christopher Guevara, David Smyth. 2023-07-19. A stratification of moduli of arbitrarily singular curves. https://arxiv.org/abs/2307.10013

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