Fano Threefolds with 2-Torus Action: A Picture Book

Hendrik Suess

Research output: Contribution to journalArticlepeer-review


Following the work of Altmann and Hausen we give a combinatorial description for smooth Fano threefolds admitting a 2-torus action. We show that a whole variety of properties and invariants can be read off from this description. As an application we prove and disprove the existence of Kähler-Einstein metrics for some of these Fano threefolds, calculate their Cox rings and some of their toric canonical degenerations.
Original languageEnglish
Pages (from-to)905-940
JournalDocumenta mathematica
Publication statusPublished - 2014


  • torus action, moment polytope, Fano variety, Kahler-Einstein metric, Cox ring


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