Geometric and arithmetic aspects of rational elliptic surfaces

2023/02/10 by Costa, Renato Dias
#11E25 #11G05 #14G05 #14J27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.05485

Abstract

PhD dissertation consists in three lines of investigation involving rational elliptic surfaces, namely 1) a study of conic bundles on these surfaces; 2) an investigation of the possible intersection numbers of two sections and 3) a theorem regarding the set of fibers whose Mordell-Weil ranks are at least 3 units higher than the generic rank of the elliptic fibration.

Related

• Elliptic Surfaces
• The Geometry and Arithmetic of Elliptic Surfaces
• Rational curves on elliptic surfaces
• Moderate rank jumps on rational elliptic surfaces via construction of conics
• Linear systems on rational elliptic surfaces and elliptic fibrations on K3 surfaces