Abstract

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.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2004-03-03

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd341

Keywords

rational elliptic surfaces, root lattice, Mordell-Weil lattice, algebraic geometry, singular fibre

Included in

Mathematics Commons

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