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Genus zero systems for primitive groups of affine type

Wang, Gehao (2012)
Ph.D. thesis, University of Birmingham.

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Abstract

Let M\(_g\) be the moduli space of genus g curves. A Hurwitz locus in M\(_g\) is a locus of points representing G-covers of fixed genus g with a given ramification type. The classification of Hurwitz loci of complex curves admitting G is by the computation of orbits of a suitable surface braid group acting on the generating tuples of G. When the genus of the curve is low, the braid orbits can be enumerated explicitly using GAP (Groups, Algorithm, Programming) computer algebra system and the BRAID package by Magaard, Shpectorov and Volklein. However, the length of the orbits dramatically increases with the size of G and genus of the curve. In order to handle larger orbits, we propose to break up the tuples into two or more shorter pieces which can be computed within reasonable time, and then recombine them together as direct products to form the braid orbits.

Type of Work:Ph.D. thesis.
Supervisor(s):Magaard, Kay (Prof) and Shpectorov, Sergey
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
QA75 Electronic computers. Computer science
Institution:University of Birmingham
ID Code:3322
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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