Return to search

On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera

Compact Riemann surfaces of genus greater than 1 can be realized as quotient spaces of the hyperbolic plane by the action of Fuchsian groups. The Teichmüller space is the set of all complex structures of Riemann surfaces and the moduli space the set of conformal equivalence classes of Riemann surfaces. For genus greater than two the branch locus of the covering of the moduli space by the Teichmüller space can be identified wi the set of Riemann surfaces admitting non-trivial automorphisms. Here we give the orbifold structure of the branch locus of surfaces of genus 5 by studying the equisymmetric stratification of the branch locus. This gives the orbifold structure of the moduli space. We also show that the strata corresponding to surfaces with automorphisms of order 2 and 3 belong to the same connected component for every genus. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-51519
Date January 2009
CreatorsBartolini, Gabriel
PublisherLinköpings universitet, Tillämpad matematik, Linköpings universitet, Tekniska högskolan, Linköping : Linköping University Electronic Press
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeLicentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess
RelationLinköping Studies in Science and Technology. Thesis, 0280-7971 ; 1413

Page generated in 0.0015 seconds