Non‐complete rational T‐varieties of complexity one

@article{Hausen2015NoncompleteRT,
  title={Non‐complete rational T‐varieties of complexity one},
  author={Juergen Hausen and Milena Wrobel},
  journal={Mathematische Nachrichten},
  year={2015},
  volume={290}
}
We consider rational varieties with a torus action of complexity one and extend the combinatorial approach via the Cox ring developed for the complete case in earlier work to the non‐complete, e.g. affine, case. This includes in particular a description of all factorially graded affine algebras of complexity one with only constant homogeneous invertible elements in terms of canonical generators and relations. 
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