K-Stability for Fano Manifolds with Torus Action of Complexity 1 (bibtex)
by Nathan Owen Ilten, Hendrik Süß
Abstract:
We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial Kahler-Ricci soliton.
Reference:
K-Stability for Fano Manifolds with Torus Action of Complexity 1 (Nathan Owen Ilten, Hendrik Süß), Duke Mathematical Journal, volume 166, 2017.  
Bibtex Entry:
@article{is17,
   author = {{Ilten}, Nathan Owen and S{\"u}{\ss}, Hendrik},
    title = "{K-Stability for Fano Manifolds with Torus Action of Complexity 1}",
  journal = {Duke Mathematical Journal},
archivePrefix = "arXiv",
   eprint = {1507.04442},
 primaryClass = "math.AG",
 keywords = {Mathematics - Algebraic Geometry, Mathematics - Differential Geometry, 32Q20, 14L30, 14J45},
     year = 2017,
     pages = {177-204},
     volume = 166,
     issue = 1,  
  gsid={1558861318587888632,5881870906665656935},
  doi={10.1215/00127094-3714864}, 
 url={http://arxiv.org/abs/1507.04442},
  abstract={We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial Kahler-Ricci soliton. },
}
 
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