## Tohoku Mathematical Journal

### Normal singularities with torus actions

#### 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, ($\boldsymbol{Q}$-)factorial, or ($\boldsymbol{Q}$-)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.

#### Article information

Source
Tohoku Math. J. (2), Volume 65, Number 1 (2013), 105-130.

Dates
First available in Project Euclid: 8 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1365452628

Digital Object Identifier
doi:10.2748/tmj/1365452628

Mathematical Reviews number (MathSciNet)
MR3049643

Zentralblatt MATH identifier
1267.14046

Subjects
Primary: Secondary

#### Citation

Liendo, Alvaro; Süss, Hendrik. Normal singularities with torus actions. Tohoku Math. J. (2) 65 (2013), no. 1, 105--130. doi:10.2748/tmj/1365452628. https://projecteuclid.org/euclid.tmj/1365452628