Rank jumps on elliptic surfaces and the Hilbert property

2019/07/03 by Daniel Loughran, Cecília Salgado, Loughran, Daniel +1 · 3 citations
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/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 1.

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• Moderate rank jumps on rational elliptic surfaces via construction of conics
• Hilbert properties of varieties
• Fermat near misses and the integral Hilbert Property

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