# Genus zero systems for primitive groups of affine type

Wang, Gehao (2012). Genus zero systems for primitive groups of affine type. University of Birmingham. Ph.D.

 Preview
Wang12PhD.pdf
PDF

## 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: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Magaard Dr, KayUNSPECIFIEDUNSPECIFIED
Shpectorov Prof., SergeyUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: None/not applicable
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
URI: http://etheses.bham.ac.uk/id/eprint/3322

### Actions

 Request a Correction View Item