Geometric and arithmetic aspects of rational elliptic surfaces

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.

arXiv commentPhD dissertation presented in December 2022 in the Federal University of Rio de Janeiro (UFRJ)