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arXiv · 2509.25432

The locus of plane curves in the moduli stack of curves

Aaron Landesman
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Abstract

Let $d \geq 4$ and let $U_d$ denote the locus of smooth curves in the Hilbert scheme of degree $d$ plane curves. If the members of $U_d$ have genus $g$, let $\mathscr{M}_g$ denote the moduli stack of genus $g$ curves. We show that the natural map $[U_d/\operatorname{PGL}_3] \to \mathscr{M}_g$ is a locally closed embedding.

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Aaron Landesman. 2025-09-29. The locus of plane curves in the moduli stack of curves. https://arxiv.org/abs/2509.25432

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