Non-thin rank jumps for double elliptic K3 surfaces

Hector Pasten, Cecília Salgado*

*Corresponding author voor dit werk

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For an elliptic surface π:X→P1 defined over a number field K, a theorem of Silverman shows that for all but finitely many fibres above K-rational points, the resulting elliptic curve over K has Mordell-Weil rank at least as large as the rank of the group of sections of π. When X is a K3 surface with two distinct elliptic fibrations, we show that the set of K-rational points of P1 for which this rank inequality is strict, is not a thin set, under certain hypothesis on the fibrations. Our results provide one of the first cases of this phenomenon beyond that of rational elliptic surfaces.

Originele taal-2English
Pagina's (van-tot)771-781
Aantal pagina's11
TijdschriftManuscripta mathematica
Volume175
Vroegere onlinedatum28-jun.-2024
DOI's
StatusPublished - nov.-2024

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