Normal singularities with torus actions

Alvaro Liendo (1) , Hendrik Süss (2)

1 IF - Institut Fourier
2 Institut für Mathematik

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.

Mots clés: torus actions; T-varieties; characterization of singularities; toroidal desingularization

Domaines: Géométrie algébrique [math.AG]

Alvaro Liendo, Hendrik Süss. Normal singularities with torus actions. 2010. ⟨hal-00483304⟩