On Terminal Fano Varieties with a Torus Action of Complexity One

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dc.contributor.advisor Hausen, Jürgen (Prof. Dr.)
dc.contributor.author Nicolussi, Michele
dc.date.accessioned 2017-07-24T07:41:52Z
dc.date.available 2017-07-24T07:41:52Z
dc.date.issued 2017-07-24
dc.identifier.other 491119534 de_DE
dc.identifier.uri http://hdl.handle.net/10900/77235
dc.identifier.uri http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-772359 de_DE
dc.identifier.uri http://dx.doi.org/10.15496/publikation-18636
dc.description.abstract In toric geometry, Fano varieties correspond to certain lattice polytopes, whose lattice points determine the type of singularities of the variety. In this spirit we approach the larger family of Fano varieties with a torus action of complexity one. After an introductory chapter in the language of Cox rings, the world of Fano varieties of complexity one is tackled with the goal of finding explicit classification for certain subfamilies. We associate to any such variety the anticanonical complex, a polyhedral complex that detects the type of singularities. This enables the classification of terminal Fano threefolds of complexity one with Picard number one and those that do not allow any divisorial contraction. Moreover the smooth (almost) Fano varieties of complexity one having Picard number two and arbitrary dimension are also classified. en
dc.language.iso en de_DE
dc.publisher Universität Tübingen de_DE
dc.rights ubt-podok de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=de de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=en en
dc.subject.classification Algebraische Geometrie de_DE
dc.subject.ddc 510 de_DE
dc.subject.other algebraic geometry en
dc.subject.other Fano varieties en
dc.subject.other Klassifikation de_DE
dc.subject.other torus action en
dc.subject.other Cox Ringe de_DE
dc.subject.other terminal singularities en
dc.subject.other terminale Singularitäten de_DE
dc.subject.other Cox rings en
dc.subject.other classification en
dc.subject.other Fano Varietäten de_DE
dc.subject.other Torus-Wirkung de_DE
dc.title On Terminal Fano Varieties with a Torus Action of Complexity One en
dc.type Dissertation de_DE
dcterms.dateAccepted 2017-06-23
utue.publikation.fachbereich Mathematik de_DE
utue.publikation.fakultaet 7 Mathematisch-Naturwissenschaftliche Fakultät de_DE

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