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Branched covering spaces of an elliptic curve that branch only above a single point

Anema, A.S.I. (2011) Branched covering spaces of an elliptic curve that branch only above a single point. Master's Thesis / Essay, Mathematics.

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Abstract

A branched covering space is a non-constant holomorphism f from a Riemann surface X to a Riemann surface Y. For almost all points x in X there exists an open set U in X containing x such that f restricts to a homeomorphism from U to f(U). However if for some x in X no such set U exists, then f is said to branch above f(x). Branched covering spaces of elliptic curves that branch only above a single point are studied in this thesis. It turns out that such spaces exist from a topological perspective and that it is possible to give an explicit example with algebraic methods. Furthermore a family of branched covering spaces of the discriminant 4a^3+27b^2=1 is analysed.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:46
Last Modified: 15 Feb 2018 07:46
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/9752

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