On isogenies among certain abelian surfaces
| Autor: | Tony Shaska, Andreas Malmendier, Adrian Clingher |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Double cover Plane (geometry) General Mathematics Mathematics::Number Theory Jacobian variety Prym variety Interpretation (model theory) Section (fiber bundle) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 14J28 14H40 Simple (abstract algebra) FOS: Mathematics Abelian group Algebraic Geometry (math.AG) Mathematics |
| Popis: | We construct a three-parameter family of non-hyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a general hyperelliptic genus-two curve. Our construction is based on the existence of special elliptic fibrations with the section on the associated Kummer surfaces that provide a simple geometric interpretation for the rational double cover induced by the two-isogeny between the abelian surfaces. 33 pages; minor typos corrected in version 2 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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