English

Large rank jumps on elliptic surfaces and the Hilbert property

Number Theory 2022-05-17 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.2205.07801,
  title  = {Large rank jumps on elliptic surfaces and the Hilbert property},
  author = {Renato Dias Costa and Cecília Salgado},
  journal= {arXiv preprint arXiv:2205.07801},
  year   = {2022}
}