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arXiv · 2411.14645

Codimension two torus actions on the affine space

Alvaro Liendo·Charlie Petitjean
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Abstract

In this paper, we classify smooth, contractible affine varieties equipped with faithful torus actions of complexity two, having a unique fixed point and a two-dimensional algebraic quotient isomorphic to a toric blow-up of a toric surface. These varieties are of particular interest as they represent the simplest candidates for potential counterexamples to the linearization conjecture in affine geometry.

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Alvaro Liendo, Charlie Petitjean. 2024-11-22. Codimension two torus actions on the affine space. https://arxiv.org/abs/2411.14645

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