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AuthorKirály, Franzdc.contributor.author
Date of accession2016-03-15T06:23:10Zdc.date.accessioned
Available in OPARU since2016-03-15T06:23:10Zdc.date.available
Year of creation2010dc.date.created
AbstractThis thesis adresses the problem of tame and wild cyclic quotient singularities of local Noetherian rings and arithmetic surfaces. In chapter 2, we study the ring of invariants of a local Noetherian ring by a tame cyclic action. We collect and generalize classic results on tame cyclic quotient singularities in the context of toric geometry. In chapter 3, we prove algebraic results on the invariant ring of a local Noetherian ring by a possibly wild cyclic action of prime order. The central result is a characterization of monogenous extensions which can be read as a regularity criterion for the invariant ring generalizing a criterion of Serre. In chapter 4, we relate the structure of a quotient singularity of a regular arithmetic surface to the action of the group on its models. In particular, we prove results relating the minimal normal crossings desingularization of the quotient to certain models of the original surface.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandard (Fassung vom 01.10.2008)dc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v2dc.rights.uri
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHArithmetical algebraic geometrydc.subject.lcsh
LCSHInvariantsdc.subject.lcsh
LCSHSingularities: Mathematicsdc.subject.lcsh
TitleWild quotient singularities of arithmetic surfaces and their regular modelsdc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-1793dc.identifier.doi
PPN640751539dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-74265dc.identifier.urn
GNDArithmetische Geometriedc.subject.gnd
GNDInvariantentheoriedc.subject.gnd
GNDSingularität <Mathematik>dc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2010-11-16T07:39:24Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionZ: J-H 13.818; N: J-H 9.884uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS-ID7426uulm.vtsID
CategoryPublikationenuulm.category
University Bibliographyjauulm.unibibliographie


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