Abstract
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 language | English |
|---|---|
| Pages (from-to) | 905-940 |
| Journal | Documenta mathematica |
| Volume | 19 |
| Publication status | Published - 2014 |
Keywords
- torus action, moment polytope, Fano variety, Kahler-Einstein metric, Cox ring