Geodesic
Fano threefolds with 2-torus action
Documenta mathematica, Tome 19 (2014), pp. 905-940
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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.
DOI : 10.4171/dm/468
Classification : 14J45, 14L30, 32Q20
Mots-clés : torus action, Fano variety, moment polytope, Kähler-Einstein metric, Cox ring 
@article{10_4171_dm_468,
     author = {Hendrik S\"u{\ss}},
     title = {Fano threefolds with 2-torus action},
     journal = {Documenta mathematica},
     pages = {905--940},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/468},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/468/}
}
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Hendrik Süß. Fano threefolds with 2-torus action. Documenta mathematica, Tome 19 (2014), pp. 905-940. doi: 10.4171/dm/468

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