A note on splitting curves of plane quartics and multi-sections of rational elliptic surfaces
| Autor: | Shinzo Bannai |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Plane (geometry)
Plane curve Group (mathematics) 010102 general mathematics Mathematical analysis Type (model theory) 01 natural sciences Supersingular elliptic curve Mathematics::Algebraic Geometry Simple (abstract algebra) 0103 physical sciences Elliptic surface 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 202:428-439 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2016.02.005 |
| Popis: | In this note, we study the relation between splitting curves of plane quartics and multi-sections of rational elliptic surfaces associated to the quartics. We give a criterion for when a simple contact curve splits and calculate the images of the components of the corresponding multi-sections in the Mordell–Weil group of the associated rational elliptic surface. We also introduce a notion called the splitting type for certain configurations of plane curves which allows us to distinguish the configurations topologically. To demonstrate its effectiveness we construct new examples of Zariski pairs and a Zariski triple. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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