Canonical divisors on T-varieties (bibtex)
by Hendrik Süß
Abstract:
Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C*-surfaces of Picard number 1 and Gorenstein index less than 4. In further examples we show how classification might work in higher dimensions and we give explicit descriptions of some equivariant smoothings of Fano threefolds.
Reference:
Canonical divisors on T-varieties (Hendrik Süß), 2008.  
Bibtex Entry:
@unpublished{canonical,
   author = {{S{\"u}{\ss}}, Hendrik},
    title = "{Canonical divisors on {T}-varieties}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {0811.0626},
 primaryClass = "math.AG",
 keywords = {Mathematics - Algebraic Geometry, 14L30, 14B05, 14M25},
     year = 2008,
    month = may,
  url = {http://arxiv.org/abs/0811.0626},
  gsid = {4026210155007546339},
  abstract = {Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C*-surfaces of Picard number 1 and Gorenstein index less than 4. In further examples we show how classification might work in higher dimensions and we give explicit descriptions of some equivariant smoothings of Fano threefolds. },
}
 
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