Fano threefolds with 2-torus action - a picture book
arXiv:1308.2379
Abstract
Following the work of Altmann and Hausen we give a combinatorial description in terms 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 Kahler-Einstein metrics for some of these Fano threefolds, calculate their Cox rings and some of their toric canonical degenerations.
26 pages, 44 figures; includes a correction to the published version