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On the Equation of an Origami of Genus two with two Cusps

Kappes, Andre

Abstract:
An origami is a compact Riemann surface provided with a flat structure that comes from a covering map to a torus. Affine variations of the flat structure lead to a family of compact Riemann surfaces whose base is an algebraic curve in the moduli space, called Teichmueller curve. The main aim of this thesis is to discuss a specific example of an origami in genus 2, and to give an explicity algebraic description for the Teichmueller curve, which by construction is an analytic object. To this end, a summary of the theory of Riemann surfaces with focus on hyperelliptic surfaces, as well as an introduction to translation surfaces, Teichmueller curves and origamis is also included.


Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Hochschulschrift
Jahr 2007
Sprache Englisch
Identifikator URN: urn:nbn:de:swb:90-289557
KITopen ID: 1000028955
Abschlussart Abschlussarbeit - Diplom
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