Date of Degree

9-2015

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Lucien Szpiro

Committee Members

Raymond Hoobler

Kenneth Kramer

Liang-Chung Hsia

Subject Categories

Mathematics

Keywords

arithmetic dynamics; binary forms; field of definition; invariant theory; moduli; rational map

Abstract

We construct the moduli space, Md, of degree d rational maps on ℙ1 in terms of invariants of binary forms. We apply this construction to give explicit invariants and equations for M3.

Using this construction, we give a method for solving the following problems: (1) explicitly construct, from a moduli point P ∈ Md(k), a rational map ∅ with the given moduli; (2) find the field of definition of a rational map ∅. We work out the method in detail for the case d = 3.

Included in

Mathematics Commons

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