The geometry of <var>T</var>-varieties
Klaus AltmannFreie Universität Berlin, Germany
Nathan IltenBonn, Germany
Lars PetersenFreie Universität Berlin, Germany
Hendrik SüßBrandenburgische Technische Universität Cottbus, Germany
Robert VollmertFreie Universität Berlin, Germany
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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.