Defining algebraic polynomials for cyclic prime covers of the Riemann sphere

Persistent Link:
http://hdl.handle.net/10150/280574
Title:
Defining algebraic polynomials for cyclic prime covers of the Riemann sphere
Author:
Wootton, Aaron
Issue Date:
2004
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A compact Riemann surface X is said to be a cyclic p-gonal surface if it admits an automorphism φ of prime order p such that the quotient space X/(φ) has genus 0. It is said to be normal cyclic p-gonal if in addition, the group generated by φ is normal in the full automorphism group of X. In the following notes, we determine a method to find defining polynomial equations for any cyclic p-gonal surface X. If the surface X is assumed to be normal cyclic p-gonal, then all redundancies--equations which are equations for the same surface up to conformal equivalence--are also found.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Lux, Klaus M.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleDefining algebraic polynomials for cyclic prime covers of the Riemann sphereen_US
dc.creatorWootton, Aaronen_US
dc.contributor.authorWootton, Aaronen_US
dc.date.issued2004en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA compact Riemann surface X is said to be a cyclic p-gonal surface if it admits an automorphism φ of prime order p such that the quotient space X/(φ) has genus 0. It is said to be normal cyclic p-gonal if in addition, the group generated by φ is normal in the full automorphism group of X. In the following notes, we determine a method to find defining polynomial equations for any cyclic p-gonal surface X. If the surface X is assumed to be normal cyclic p-gonal, then all redundancies--equations which are equations for the same surface up to conformal equivalence--are also found.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLux, Klaus M.en_US
dc.identifier.proquest3132270en_US
dc.identifier.bibrecord.b46707669en_US
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