Codimension two torus actions on the affine space
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910708435779584 |
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| author | Liendo, Alvaro Petitjean, Charlie |
| author_facet | Liendo, Alvaro Petitjean, Charlie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codimension two torus actions on the affine space Liendo, Alvaro Petitjean, Charlie Algebraic Geometry 14L30, 14R05, 14R10, 14R20 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. |
| title | Codimension two torus actions on the affine space |
| topic | Algebraic Geometry 14L30, 14R05, 14R10, 14R20 |
| url | https://arxiv.org/abs/2411.14645 |