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Elliptic normal curves of even degree and theta functions.
- Source :
-
Research in Number Theory . 6/21/2024, Vol. 10 Issue 3, p1-37. 37p. - Publication Year :
- 2024
-
Abstract
- An elliptic curve E can be immersed in P N - 1 as a curve of degree N by means of the linear system of |NO|, where O is the origin of E. Well-known classical results going back to Bianchi and Klein say that if N is odd, this immersion is uniquely determined by specifying a full-level N structure. In this paper we show that if N is even, uniqueness of immersion is ensured by specifying a level structure associated with a certain congruence subgroup between Γ (N) and Γ (2 N) . Moreover, we construct, over the complex number field, an immersion by means of suitably chosen theta functions, and write down the quadratic equations satisfied by them. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 10
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 178028628
- Full Text :
- https://doi.org/10.1007/s40993-024-00547-0