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AuthorSteinle, Thomasdc.contributor.author
Date of accession2016-03-15T10:40:24Zdc.date.accessioned
Available in OPARU since2016-03-15T10:40:24Zdc.date.available
Year of creation2015dc.date.created
AbstractA Teichmüller curve is a curve embedded in the moduli space of smooth projective curves of genus g which is totally geodesic for the Teichmüller metric. In this thesis we construct a new class of Teichmüller curves, using a characterisation due to Martin Möller. This involves constructing a suitable one-dimensional family of smooth projective curves parametrised by the points of a Teichmüller. We show that our new Teichmüller curves are the last Teichmüller curves in a larger class of Teichmüller curves constructed by Irene Bouw and Martin Möller. About candidates for further Teichmüller curves not much is known. A starting point may be the following observation. The points of a Teichmüller curve correspond to curves with real multiplication by large totally real number fields. Jordan Ellenberg constructs three one-dimensional families with this property. However, in this thesis we show that, except for some special cases, Ellenberg"s families do not define Teichmüller curves. To do this, we interpret them as families over suitable Hurwitz spaces. We then describe a criterion to check whether a family of curves does not define a Teichmüller curve by studying the boundary of the associated Hurwitz space and apply this criterion for exclusion to Ellenberg"s families. We moreover show how to modify Ellenberg"s families by passing to an adapted Hurwitz space in such a way that the criterion for exclusion no longer holds. It remains open whether this modification indeed produces Teichmüller curves.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseCC BY 3.0 Unporteddc.rights
Link to license texthttp://creativecommons.org/licenses/by/3.0/dc.rights.uri
KeywordAlgebraic curvesdc.subject
KeywordHurwitz spacesdc.subject
KeywordTeichmüller curvesdc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
TitleTeichmüller curves and Hurwitz spacesdc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-3285dc.identifier.doi
PPN839411731dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-97735dc.identifier.urn
GNDAlgebraische Kurvedc.subject.gnd
GNDHurwitz-Raumdc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2015-11-10T09:26:43Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionW: W-H 14.448uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS ID9773uulm.vtsID
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


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