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arXiv · 2005.12449

Elliptic normal curves of even degree and theta functions

Masanobu Kaneko·Masato Kuwata
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Abstract

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.

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Masanobu Kaneko, Masato Kuwata. 2023-04-01. Elliptic normal curves of even degree and theta functions. https://doi.org/10.1007/s40993-024-00547-0

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