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2013 Normal singularities with torus actions
Alvaro Liendo, Hendrik Süss
Tohoku Math. J. (2) 65(1): 105-130 (2013). DOI: 10.2748/tmj/1365452628

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.

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Alvaro Liendo. Hendrik Süss. "Normal singularities with torus actions." Tohoku Math. J. (2) 65 (1) 105 - 130, 2013. https://doi.org/10.2748/tmj/1365452628

Information

Published: 2013
First available in Project Euclid: 8 April 2013

zbMATH: 1267.14046
MathSciNet: MR3049643
Digital Object Identifier: 10.2748/tmj/1365452628

Subjects:
Primary: Secondary

Rights: Copyright © 2013 Tohoku University

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Vol.65 • No. 1 • 2013
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