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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2005.12449 |
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| _version_ | 1866910497841872896 |
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| author | Kaneko, Masanobu Kuwata, Masato |
| author_facet | Kaneko, Masanobu Kuwata, Masato |
| contents | An elliptic curve may be immersed in ${\mathbf{P}}^{N-1}$ as a degree $N$ curve using level $N$ structure. In the case where $N$ is odd, there are well known classical results dating back to Bianchi and Klein. In this paper we study the case of even $N$ in some detail. In particular, over the complex number field, we define an immersion using suitably chosen theta functions, and study the quadratic equations satisfied by them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_12449 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Elliptic normal curves of even degree and theta functions Kaneko, Masanobu Kuwata, Masato Number Theory 14H52 (Primary) 14H42, 11F11 (Secondary) An elliptic curve may be immersed in ${\mathbf{P}}^{N-1}$ as a degree $N$ curve using level $N$ structure. In the case where $N$ is odd, there are well known classical results dating back to Bianchi and Klein. In this paper we study the case of even $N$ in some detail. In particular, over the complex number field, we define an immersion using suitably chosen theta functions, and study the quadratic equations satisfied by them. |
| title | Elliptic normal curves of even degree and theta functions |
| topic | Number Theory 14H52 (Primary) 14H42, 11F11 (Secondary) |
| url | https://arxiv.org/abs/2005.12449 |