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Type: Thesis
Title: Holomorphic Immersions of Restricted Growth from Smooth Affine Algebraic Curves into the Complex Plane
Author: John, Daniel
Issue Date: 2019
School/Discipline: School of Mathematical Sciences
Abstract: We investigate immersions of restricted growth from affine curves into the complex plane. We focus on the finite order and algebraic categories. In the finite order case we prove a generalisation of a result due to Forstneric and Ohsawa, showing that on every affine curve there is a finite order 1-form with prescribed periods and divisor, provided we restrict the growth of the divisor at the punctures. We also enumerate the algebraic immersions of triply punctured compact surfaces into the complex plane using the theory of dessins d’enfants and obtain an upper bound on the number of surfaces that admit such an immersion.
Advisor: Larusson, Finnur
Stevenson, Daniel
Dissertation Note: Thesis (MPhil.) -- University of Adelaide, School of Mathematical Sciences, 2019
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