Structural properties of Cox rings of T-varieties

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dc.contributor.advisor Hausen, Jürgen (Prof. Dr.) Wrobel, Milena 2018-05-15T10:37:24Z 2018-05-15T10:37:24Z 2018
dc.identifier.other 507573641 de_DE
dc.identifier.uri de_DE
dc.description.abstract In the present thesis we generalize the Cox ring based description for complete rational varieties with torus action of complexity one to Mori dream spaces with effective torus action of arbitrary high complexity. In the first part of this thesis we complete the picture for varieties of complexity one by treating the non complete, e.g affine, case. With this approach to affine varieties with torus action of complexity one, we characterize iterability of Cox rings in numerical terms. This enables us to regard log terminal singularities of arbitrary dimension with torus action of complexity one, in a larger sense, as quotient singularities, comparable to the well known surface case. In the second part, we present a constructive approach to Cox rings of Mori dream spaces with a torus action of arbitrary complexity. We study a sample class comprising the complexity one case, the so called arrangement varieties, and give concrete classification results for Fano arrangement varieties of Picard number one and for Fano arrangement varieties of complexity and Picard number two. en
dc.language.iso en de_DE
dc.publisher Universität Tübingen de_DE
dc.rights ubt-podok de_DE
dc.rights.uri de_DE
dc.rights.uri en
dc.subject.classification Algebraische Geometrie , Torische Varietät , Algebraische Varietät , Geometrische Invariantentheorie de_DE
dc.subject.ddc 510 de_DE
dc.subject.other Cox ring en
dc.subject.other T-variety en
dc.subject.other Torus-Wirkung de_DE
dc.subject.other torus action en
dc.subject.other iteration of Cox rings en
dc.subject.other Iteration von Cox-Ringen de_DE
dc.subject.other higher complexity en
dc.subject.other log terminal de_DE
dc.subject.other Fano variety en
dc.subject.other höhere Komplexität de_DE
dc.subject.other Fano-Varietät de_DE
dc.subject.other classification en
dc.subject.other Klassifikation de_DE
dc.subject.other Cox-Ringe de_DE
dc.subject.other T-Varietät de_DE
dc.title Structural properties of Cox rings of T-varieties en
dc.type PhDThesis de_DE
dcterms.dateAccepted 2018-03-16
utue.publikation.fachbereich Mathematik de_DE
utue.publikation.fakultaet 7 Mathematisch-Naturwissenschaftliche Fakultät de_DE


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