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We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalizedcurves" 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 graphsand prove that each stratum $\mathscr{E}_{\Gamma}$ is a fiber bundle over afinite quotient of a product of $\mathcal{M}_{g,n}$'s. The fibers are modulischemes parametrizing subalgebras of a fixed algebra, and are in principleexplicitly computable as locally closed subschemes of products ofGrassmannians. We thus obtain a remarkably explicit geometric description ofmoduli of reduced curves with arbitrary singularities.

A stratification of moduli of arbitrarily singular curves