The $p$-rank stratification of the moduli space of double covers of a fixed elliptic curve
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911474828443648 |
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| author | Chang, Kevin Dragutinović, Dušan Groen, Steven R. Lin, Yuxin Pacheco-Tallaj, Natalia Singhal, Deepesh |
| author_facet | Chang, Kevin Dragutinović, Dušan Groen, Steven R. Lin, Yuxin Pacheco-Tallaj, Natalia Singhal, Deepesh |
| contents | In this paper we investigate the $p$-rank stratification of the moduli space of curves of genus $g$ that admit a double cover to a fixed elliptic curve $E$ in characteristic $p>2$. We show that the closed $p$-rank strata of this moduli space are equidimensional of the expected dimension. We also show the existence of a smooth double cover of $E$ of all the possible values of the $p$-rank on this moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $p$-rank stratification of the moduli space of double covers of a fixed elliptic curve Chang, Kevin Dragutinović, Dušan Groen, Steven R. Lin, Yuxin Pacheco-Tallaj, Natalia Singhal, Deepesh Number Theory Algebraic Geometry 14H10 (Primary) 14G17, 14H30, 14H40 (Secondary) In this paper we investigate the $p$-rank stratification of the moduli space of curves of genus $g$ that admit a double cover to a fixed elliptic curve $E$ in characteristic $p>2$. We show that the closed $p$-rank strata of this moduli space are equidimensional of the expected dimension. We also show the existence of a smooth double cover of $E$ of all the possible values of the $p$-rank on this moduli space. |
| title | The $p$-rank stratification of the moduli space of double covers of a fixed elliptic curve |
| topic | Number Theory Algebraic Geometry 14H10 (Primary) 14G17, 14H30, 14H40 (Secondary) |
| url | https://arxiv.org/abs/2502.09540 |