A stratification of moduli of arbitrarily singular curves

2023/07/19 by Sebastian Bozlee, Bozlee, Sebastian, Christopher A. Guevara +5
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #math.AG

paper · pdf · doi:10.48550/arxiv.2307.10013

openalex publication_date 2023/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We introduce a new moduli stack \mathscrE_g,n of "equinormalized curves," closely related to the moduli space of all reduced, connected algebraic curves. We construct a stratification \bigsqcup_Γ\mathscrE_Γ of \mathscrE_g,n indexed by generalized dual graphs and prove that each stratum \mathscrE_Γ is a fiber bundle over a finite quotient of a product of \moduli_g,ns. 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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