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On the Branch Loci of Moduli Spaces of Riemann SurfacesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Linköping: Linköping University Electronic Press, 2012. , p. 45
##### Series

Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1440
##### National Category

Geometry
##### Identifiers

URN: urn:nbn:se:liu:diva-77449ISBN: 978-91-7519-913-9 (print)OAI: oai:DiVA.org:liu-77449DiVA, id: diva2:527079
##### Public defence

2012-06-05, Planck, Fysikhuset, ingång 57, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
##### Opponent

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#####

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Available from: 2012-06-05 Created: 2012-05-16 Last updated: 2015-03-09Bibliographically approved
##### List of papers

The spaces of conformally equivalent Riemann surfaces, *M _{g}* where

**Paper 1.** In this paper we show that the strata corresponding to actions of order 2 and 3 belong to the same connected component for arbitrary genera. 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.

**Paper 2.** This paper contains a collection of results regarding components of the branch loci, some of them proved in detail in other papers. It is shown that for any integer d if p is a prime such that p > (*d* + 2)^{2}, there there exist isolated strata of dimension *d* in the moduli space of Riemann surfaces of genus (*d* + 1)(*p* − 1)/2. It is also shown that if we consider Riemann surfaces as Klein surfaces, the branch loci are connected for every genera due to reflections.

**Paper 3.** Here we consider surfaces of genus 4 and 5. Here we study the automorphism groups of Riemann surfaces of genus 4 and 5 up to topological equivalence and determine the complete structure of the equisymmetric stratification of the branch locus.

**Paper 4.** In this paper we establish that the connectedness of the branch loci is a phenomenon for low genera. More precisely we prove that the only genera *g* where *B _{g}* is connected are

1. On the connectedness of the branch locus of the moduli space of Riemann surfaces$(function(){PrimeFaces.cw("OverlayPanel","overlay310868",{id:"formSmash:j_idt626:0:j_idt630",widgetVar:"overlay310868",target:"formSmash:j_idt626:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus$(function(){PrimeFaces.cw("OverlayPanel","overlay468692",{id:"formSmash:j_idt626:1:j_idt630",widgetVar:"overlay468692",target:"formSmash:j_idt626:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. On the Orbifold Structure of the Moduli Space of Riemann Surfaces of Genera Four and Five$(function(){PrimeFaces.cw("OverlayPanel","overlay530789",{id:"formSmash:j_idt626:2:j_idt630",widgetVar:"overlay530789",target:"formSmash:j_idt626:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. On the connected branch loci of moduli spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay530790",{id:"formSmash:j_idt626:3:j_idt630",widgetVar:"overlay530790",target:"formSmash:j_idt626:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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