Large rank jumps on elliptic surfaces and the Hilbert property

Renato Dias Costa, Cecília Salgado

Published 2022-05-16Version 1

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.