Van Geemen--Sarti involutions and elliptic fibrations on K3 surfaces\n double cover of \ℙ²

2011/10/28 by Paola Comparin, Comparin, Paola, Alice Garbagnati +1
Mathematics · #14J27 #14J28 #14J50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1110.6380

openalex publication_date 2011/10/28 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper we classify the elliptic fibrations on K3 surfaces which are\nthe double cover of a blow up of \ℙ² branched along rational curves\nand we give equations for many of these elliptic fibrations. Thus we obtain a\nclassification of the van Geemen--Sarti involutions (which are symplectic\ninvolutions induced by a translation by a 2-torsion section on an elliptic\nfibration) on such a surface. Each van Geemen--Sarti involution induces a\n2-isogeny between two K3 surfaces, which is described in this paper.\n

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