Kummer Surfaces, Isogenies and Theta Functions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914159436759040 |
|---|---|
| author | Clingher, Adrian Malmendier, Andreas Shaska, Tony |
| author_facet | Clingher, Adrian Malmendier, Andreas Shaska, Tony |
| contents | The paper discusses geometric and computational aspects associated with $(n,n)$-isogenies for principally polarized Abelian surfaces and related Kummer surfaces. We start by reviewing the comprehensive Theta function framework for classifying genus-two curves, their principally polarized Jacobians, as well as for establishing explicit quartic normal forms for associated Kummer surfaces. This framework is then used for practical isogeny computations. A particular focus of the discussion is the $(n,n)$-Split isogeny case. We also explore possible extensions of Richelot's $(2,2)$-isogenies to higher order cases, with a view towards developing efficient isogeny computation algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kummer Surfaces, Isogenies and Theta Functions Clingher, Adrian Malmendier, Andreas Shaska, Tony Algebraic Geometry 14J28, 14K02, 14K25 The paper discusses geometric and computational aspects associated with $(n,n)$-isogenies for principally polarized Abelian surfaces and related Kummer surfaces. We start by reviewing the comprehensive Theta function framework for classifying genus-two curves, their principally polarized Jacobians, as well as for establishing explicit quartic normal forms for associated Kummer surfaces. This framework is then used for practical isogeny computations. A particular focus of the discussion is the $(n,n)$-Split isogeny case. We also explore possible extensions of Richelot's $(2,2)$-isogenies to higher order cases, with a view towards developing efficient isogeny computation algorithms. |
| title | Kummer Surfaces, Isogenies and Theta Functions |
| topic | Algebraic Geometry 14J28, 14K02, 14K25 |
| url | https://arxiv.org/abs/2505.13727 |