Rank jumps on elliptic surfaces and the Hilbert property
arXiv:1907.01987
Abstract
Given an elliptic surface over a number field, we study the collection of fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable assumptions, we show that this collection is not thin. Our results apply to quadratic twist families and del Pezzo surfaces of degree .
16 pages. Annales de l'institut Fourier, to appear