Abelian surfaces in Hesse form and explicit isogeny formulas
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915719307853824 |
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| author | Decru, Thomas Kunzweiler, Sabrina |
| author_facet | Decru, Thomas Kunzweiler, Sabrina |
| contents | We develop a new method for the computation of $(3,3)$-isogenies between principally polarized abelian surfaces. The idea is to work with models in $\mathbb{P}^8$ induced by a symmetric level-$3$ theta structure. In this setting, the action of three-torsion points is linear, and the isogeny formulas can be described in a simple way as the composition of easy-to-evaluate maps. In the description of these formulas, the relation with the Burkhardt quartic threefold plays an important role. Furthermore, we discuss generalizations of the idea to higher dimensions as well as different isogeny degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05922 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Abelian surfaces in Hesse form and explicit isogeny formulas Decru, Thomas Kunzweiler, Sabrina Algebraic Geometry Number Theory 11G10, 14K02, 14K25 We develop a new method for the computation of $(3,3)$-isogenies between principally polarized abelian surfaces. The idea is to work with models in $\mathbb{P}^8$ induced by a symmetric level-$3$ theta structure. In this setting, the action of three-torsion points is linear, and the isogeny formulas can be described in a simple way as the composition of easy-to-evaluate maps. In the description of these formulas, the relation with the Burkhardt quartic threefold plays an important role. Furthermore, we discuss generalizations of the idea to higher dimensions as well as different isogeny degrees. |
| title | Abelian surfaces in Hesse form and explicit isogeny formulas |
| topic | Algebraic Geometry Number Theory 11G10, 14K02, 14K25 |
| url | https://arxiv.org/abs/2601.05922 |