Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916509889069056 |
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| author | Hase-Liu, Matthew Mattoo, Amal |
| author_facet | Hase-Liu, Matthew Mattoo, Amal |
| contents | We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces Hase-Liu, Matthew Mattoo, Amal Algebraic Geometry We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular locus. |
| title | Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.04618 |