Large rank jumps on elliptic surfaces and the Hilbert property

Renato Dias Costa; Cecília Salgado

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arXiv · 2205.07801

Large rank jumps on elliptic surfaces and the Hilbert property

Renato Dias Costa·Cecília Salgado

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Abstract

Given a rational elliptic surface over a number field, we study the collection of fibers whose Mordell--Weil rank is greater than the generic rank. We give conditions on the singular fibers to assure that the collection of fibers for which the rank jumps of at least 3 is not thin.

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Renato Dias Costa, Cecília Salgado. 2022-05-16. Large rank jumps on elliptic surfaces and the Hilbert property. https://arxiv.org/abs/2205.07801

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