Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771898 | Journal of Algebra | 2017 | 15 Pages |
Abstract
In this paper we provide a characterization of smooth algebraic varieties endowed with a faithful algebraic torus action in terms of a combinatorial description given by Altmann and Hausen. Our main result is that such a variety X is smooth if and only if it is locally isomorphic in the étale topology to the affine space endowed with a linear torus action. Furthermore, this is the case if and only if the combinatorial data describing X is locally isomorphic in the étale topology to the combinatorial data describing affine space endowed with a linear torus action. Finally, we provide an effective method to check the smoothness of a Gm-threefold in terms of the combinatorial data.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alvaro Liendo, Charlie Petitjean,