Smooth varieties with torus actions

Alvaro Liendo; Charlie Petitjean

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arXiv · 1606.06628

Smooth varieties with torus actions

Alvaro Liendo·Charlie Petitjean

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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 \'etale 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 \'etale 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.

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BibTeX RIS

Alvaro Liendo, Charlie Petitjean. 2016-06-21. Smooth varieties with torus actions. https://arxiv.org/abs/1606.06628

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