The Geometry of T-Varieties
  This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include singularities, separatedness and properness, divisors and intersection theory, cohomology, Cox rings, polarizations, and equivariant deformations, among others. 
Klaus Altmann, Nathan Owen Ilten, Lars Petersen, Hendrik S\"u{\ss},   Robert Vollmert
math.AG