Normal singularities with torus actions (bibtex)

by Alvaro Liendo, Hendrik Süß

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, (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.

Reference:

Normal singularities with torus actions (Alvaro Liendo, Hendrik Süß), Tohoku Mathematical Journal, volume 65, 2013.

Bibtex Entry:

@article{tsing, author = {{Liendo}, Alvaro and {S{\"u}{\ss}}, Hendrik}, title = "{Normal singularities with torus actions}", doi={10.2748/tmj/1365452628}, journal = {Tohoku Mathematical Journal}, archivePrefix = "arXiv", eprint = {1005.2462}, primaryClass = "math.AG", keywords = {Mathematics - Algebraic Geometry, 14L30, 14B05, 14M25}, year = 2013, month = jan, pages = {105-130} , volume = 65, issue = 1, url = {http://arxiv.org/abs/1005.2462}, gsid={13924844087682941334}, 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, (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. }, }

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