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On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
2009 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

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.

sted, utgiver, år, opplag, sider
Linköping: Linköping University Electronic Press , 2009. , s. 48
Serie
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1413
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-51519Lokal ID: LIU-TEK-LIC-2009:21ISBN: 978-91-7393-532-6 (tryckt)OAI: oai:DiVA.org:liu-51519DiVA, id: diva2:275389
Presentation
2009-11-23, Glashuset., Campus Valla, Linköpings universitet, Linköping, 13:15 (engelsk)
Veileder
Tilgjengelig fra: 2009-11-05 Laget: 2009-11-05 Sist oppdatert: 2020-03-10bibliografisk kontrollert
Delarbeid
1. On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
Åpne denne publikasjonen i ny fane eller vindu >>On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
2012 (engelsk)Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, nr 1, s. 35-45Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Let be an integer and let , where denotes the moduli space of compact Riemann surfaces of genus . Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space, we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belong to the same connected component. We also prove the connectedness of for and with the exception of the isolated points given by Kulkarni.

sted, utgiver, år, opplag, sider
American Mathematical Society, 2012
Emneord
Moduli spaces, Teichmüller modular group, automorphism group
HSV kategori
Identifikatorer
urn:nbn:se:liu:diva-73196 (URN)10.1090/S0002-9939-2011-10881-5 (DOI)000299596000004 ()
Forskningsfinansiär
Swedish Research Council, 621-2007-6240
Tilgjengelig fra: 2011-12-21 Laget: 2011-12-21 Sist oppdatert: 2018-09-01

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On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera(382 kB)749 nedlastinger
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