Large rank jumps on elliptic surfaces and the Hilbert property

2022/05/16 by Costa, Renato Dias, Salgado, Cecília · 2 citations
#11G05 #14G05 #14J27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2205.07801

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.

Cited by

• Moderate rank jumps on rational elliptic surfaces via construction of conics
• Hilbert properties of varieties

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