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On the existence of connected components of dimension one in the branch locus of moduli spaces of Riemann surfaces
UNED, Madrid, Spain .
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9557-9566
2012 (English)In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 111, no 1, 53-64 p.Article in journal (Refereed) Published
Abstract [en]

 Let g be an integer >= 3 and let B-g = {X is an element of mu(g) : Aut(X) not equal Id} be the branch locus of mu(g), where mu(g) denotes the moduli space of compact Riemann surfaces of genus g. The structure of B-g is of substantial interest because B-g corresponds to the singularities of the action of the modular group on the Teichmuller space of surfaces of genus g (see [14]).

Kulkarni ([15], see also [13]) proved the existence of isolated points in the branch loci of the moduli spaces of Riemann surfaces. In this work we study the isolated connected components of dimension 1 in such loci. These isolated components of dimension one appear if the genus is g = p - 1 with p prime >= 11. We use uniformization by Fuchsian groups and the equisymmetric stratification of the branch loci.

Place, publisher, year, edition, pages
2012. Vol. 111, no 1, 53-64 p.
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-88674ISI: 000313542800004OAI: diva2:605474
Available from: 2013-02-14 Created: 2013-02-14 Last updated: 2015-03-09

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