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Lattices And Their Applications To Rational Elliptic Surfaces, Gretchen Rimmasch
Lattices And Their Applications To Rational Elliptic Surfaces, Gretchen Rimmasch
Theses and Dissertations
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.