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|Title:||Holomorphic Immersions of Restricted Growth from Smooth Affine Algebraic Curves into the Complex Plane|
|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.|
|Dissertation Note:||Thesis (MPhil.) -- University of Adelaide, School of Mathematical Sciences, 2019|
|Provenance:||This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals|
|Appears in Collections:||Research Theses|
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