Rank jumps on elliptic surfaces and the Hilbert property
Number Theory
2020-11-26 v2 Algebraic Geometry
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 .
Keywords
Cite
@article{arxiv.1907.01987,
title = {Rank jumps on elliptic surfaces and the Hilbert property},
author = {Daniel Loughran and Cecília Salgado},
journal= {arXiv preprint arXiv:1907.01987},
year = {2020}
}
Comments
16 pages. Annales de l'institut Fourier, to appear