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On the rank of the fibers of elliptic K3 surfaces

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Abstract

Let X be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations π i , i = 1, 2, defined over a number field k. We prove that there is an elliptic curve C ⊂ X such that the generic rank over k of X after a base extension by C is strictly larger than the generic rank of X. Moreover, if the generic rank of π j is positive then there are infinitely many fibers of π i (j ≠ i) with rank at least the generic rank of π i plus one.

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  1. Mathematisch Instituut Leiden, Niels Bohrweg 1, Leiden, Netherlands

    Cecilia Salgado

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  1. Cecilia Salgado
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Correspondence to Cecilia Salgado.

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Salgado, C. On the rank of the fibers of elliptic K3 surfaces. Bull Braz Math Soc, New Series 43, 7–16 (2012). https://doi.org/10.1007/s00574-012-0002-6

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  • DOI: https://doi.org/10.1007/s00574-012-0002-6

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