On Terminal Fano Varieties with a Torus Action of Complexity One

DSpace Repository


URI: http://hdl.handle.net/10900/77235
Dokumentart: Dissertation
Date: 2017-07-24
Language: English
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Mathematik
Advisor: Hausen, Jürgen (Prof. Dr.)
Day of Oral Examination: 2017-06-23
DDC Classifikation: 510 - Mathematics
Keywords: Algebraische Geometrie
Other Keywords: Klassifikation
Cox Ringe
terminale Singularitäten
Fano Varietäten
algebraic geometry
Fano varieties
torus action
terminal singularities
Cox rings
License: Publishing license including print on demand
Order a printed copy: Print-on-Demand
Show full item record


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.

This item appears in the following Collection(s)