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arXiv · 1005.2462

Normal singularities with torus actions

Alvaro Liendo·Hendrik Süß
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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, (QQ-)factorial, or (QQ-)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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Alvaro Liendo, Hendrik Süß. 2010-06-08. Normal singularities with torus actions. https://doi.org/10.2748/tmj%2F1365452628

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