Lattices and Their Applications to Rational Elliptic Surfaces

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.

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Rimmasch, Gretchen

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

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/18

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1017