4 papers
Geometric and arithmetic aspects of rational elliptic surfaces
Renato Dias Costa
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 pos…
Gaps on the intersection numbers of sections on a rational elliptic surface
Renato Dias Costa
Given a rational elliptic surface X over an algebraically closed field, we investigate whether a given natural number k can be the intersection number of two sections of X. If not,…
Classification of conic bundles on a rational elliptic surface in any characteristic
Renato Dias Costa
Let be a rational elliptic surface with elliptic fibration over an algebraically closed field of any characteristic. Given a conic bundle $φ:X\to\Bbb{P}^1…
Large rank jumps on elliptic surfaces and the Hilbert property
Renato Dias Costa, Cecília Salgado
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 singul…