The Kodaira classification of the moduli space of pointed curves in genus $3$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912457768828928 |
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| author | de Preter, Ruben |
| author_facet | de Preter, Ruben |
| contents | We complete the Kodaira classification of the moduli spaces $\overline{\mathcal{M}}_{g,n}$ of curves with marked points in genus $g=3$, by proving that $\overline{\mathcal{M}}_{3,n}$ is of general type for $n \geq 15$. We prove that the singularities of $\overline{\mathcal{M}}_{3,n}$ impose no adjunction conditions for $n \geq 1$ and that the canonical class of $\overline{\mathcal{M}}_{3,n}$ is big for $n \geq 15$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Kodaira classification of the moduli space of pointed curves in genus $3$ de Preter, Ruben Algebraic Geometry We complete the Kodaira classification of the moduli spaces $\overline{\mathcal{M}}_{g,n}$ of curves with marked points in genus $g=3$, by proving that $\overline{\mathcal{M}}_{3,n}$ is of general type for $n \geq 15$. We prove that the singularities of $\overline{\mathcal{M}}_{3,n}$ impose no adjunction conditions for $n \geq 1$ and that the canonical class of $\overline{\mathcal{M}}_{3,n}$ is big for $n \geq 15$. |
| title | The Kodaira classification of the moduli space of pointed curves in genus $3$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.23812 |