This thesis discusses some of the invariants of rational elliptic surfaces, namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will then be applied to determine the groups and lattices associated with a given rational elliptic surface, along with a discussion of the uses of these groups and lattices in classifying surfaces.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Rimmasch, Gretchen, "Lattices and Their Applications to Rational Elliptic Surfaces" (2004). All Theses and Dissertations. 18.
rational elliptic surfaces, root lattice, Mordell-Weil lattice, algebraic geometry, singular fibre