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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2603.10181 |
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| _version_ | 1866918381861470208 |
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| author | Syed, Tariq |
| author_facet | Syed, Tariq |
| contents | Let $k$ be an algebraically closed base field of characteristic $0$ and let $α_{1}, α_{2}, α_{3}, d \geq 2$ be integers such that $α_{1}, α_{2}, α_{3}$ are pairwise coprime and $gcd (α_{1},d-1) = 1$. Then consider the Koras-Russell threefold $Y := \{ x + x^d y^{α_{1}} + z^{α_{2}} + t^{α_{3}} = 0\} \subset \mathbb{A}^{4}_{k}$. We prove that the Chow groups $CH^{i}(Y)$ are trivial for $i=1,2,3$ and therefore all algebraic vector bundles over $Y$ are trivial. If $α_{1}$ is odd, we also prove that the Chow-Witt groups $\widetilde{CH}^{i}(Y, \mathcal{L})$ are trivial for $i=1,2,3$ and any line bundle $\mathcal{L}$ over $Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10181 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vector bundles over certain Koras-Russell threefolds of the third kind Syed, Tariq Algebraic Geometry K-Theory and Homology Let $k$ be an algebraically closed base field of characteristic $0$ and let $α_{1}, α_{2}, α_{3}, d \geq 2$ be integers such that $α_{1}, α_{2}, α_{3}$ are pairwise coprime and $gcd (α_{1},d-1) = 1$. Then consider the Koras-Russell threefold $Y := \{ x + x^d y^{α_{1}} + z^{α_{2}} + t^{α_{3}} = 0\} \subset \mathbb{A}^{4}_{k}$. We prove that the Chow groups $CH^{i}(Y)$ are trivial for $i=1,2,3$ and therefore all algebraic vector bundles over $Y$ are trivial. If $α_{1}$ is odd, we also prove that the Chow-Witt groups $\widetilde{CH}^{i}(Y, \mathcal{L})$ are trivial for $i=1,2,3$ and any line bundle $\mathcal{L}$ over $Y$. |
| title | Vector bundles over certain Koras-Russell threefolds of the third kind |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2603.10181 |