The locus of plane curves in the moduli stack of curves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909815341580288 |
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| author | Landesman, Aaron |
| author_facet | Landesman, Aaron |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The locus of plane curves in the moduli stack of curves Landesman, Aaron Algebraic Geometry 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. |
| title | The locus of plane curves in the moduli stack of curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.25432 |