Bulletin of the London Mathematical Society · 2006 · 18 citations · 6 references
Natural SciencesPhysics3D ModelingGeometrySurface ScienceAlgebraic GeometryArithmetic GeometryElliptic CurvesSurface StructureElliptic Curve FamiliesElliptic Curve IsogeniesElliptic Curves In GeometryIsogeny ComputationKummer Theory
In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one-parameter family in terms of those of a particular family of elliptic curves. The Tate conjecture predicts the existence of a correspondence between these K3 surfaces and certain Kummer surfaces related to these elliptic curves. A geometric construction of this correspondence is given here, using results of D. Morrison on Nikulin involutions. 2000 Mathematics Subject Classification 14J27, 14G25, 14J28.
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