Van Geemen-Sarti involutions and elliptic fibrations on $K3$ surfaces double cover of $\mathbb{P}^2$
| Autor: | Alice Garbagnati, Paola Comparin |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
automorphisms of $K3$ surfaces
14J50 Surface (mathematics) 14J28 14J27 14J50 Pure mathematics Double cover symplectic involutions General Mathematics isogenies Fibration elliptic fibrations Translation (geometry) Section (fiber bundle) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry FOS: Mathematics 14J27 14J28 Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry $K3$ surfaces van Geemen-Sarti involutions Mathematics Symplectic geometry |
| Zdroj: | J. Math. Soc. Japan 66, no. 2 (2014), 479-522 |
| ISSN: | 0025-5645 |
| Popis: | In this paper we classify the elliptic fibrations on K3 surfaces which are the double cover of a blow up of $\mathbb{P}^2$ branched along rational curves and we give equations for many of these elliptic fibrations. Thus we obtain a classification of the van Geemen--Sarti involutions (which are symplectic involutions induced by a translation by a 2-torsion section on an elliptic fibration) on such a surface. Each van Geemen--Sarti involution induces a 2-isogeny between two K3 surfaces, which is described in this paper. 37 pages |
| Databáze: | OpenAIRE |
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