Normal singularities with torus actions (bibtex)
by Alvaro Liendo, Hendrik Süß
Abstract:
We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of X. In particular, we give criteria for X to have only rational, (Q-)factorial, or (Q-)Gorenstein singularities. We also give partial criteria for X to be Cohen-Macaulay or log-terminal. Finally, we provide a method to construct factorial affine varieties with a torus action. This leads to a full classification of such varieties in the case where the action is of complexity one.
Reference:
Normal singularities with torus actions (Alvaro Liendo, Hendrik Süß), Tohoku Mathematical Journal, volume 65, 2013.  
Bibtex Entry:
@article{tsing,
   author = {{Liendo}, Alvaro and {S{\"u}{\ss}}, Hendrik},
   title = "{Normal singularities with torus actions}",
   doi={10.2748/tmj/1365452628}, 
   journal = {Tohoku Mathematical Journal},
   archivePrefix = "arXiv",
   eprint = {1005.2462},
   primaryClass = "math.AG", 
   keywords = {Mathematics - Algebraic Geometry, 14L30, 14B05, 14M25},
   year = 2013,
   month = jan,
   pages = {105-130} , 
   volume = 65,  
   issue = 1,
   url = {http://arxiv.org/abs/1005.2462},
   gsid={13924844087682941334},
  abstract = {We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of X. In particular, we give criteria for X to have only rational, (Q-)factorial, or (Q-)Gorenstein singularities. We also give partial criteria for X to be Cohen-Macaulay or log-terminal. Finally, we provide a method to construct factorial affine varieties with a torus action. This leads to a full classification of such varieties in the case where the action is of complexity one. },
}
 
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