Symplectic orbits of unimodular rows
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913229818560512 |
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| author | Syed, Tariq |
| author_facet | Syed, Tariq |
| contents | For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $χ$ of rank $2n$, the group $Sp(χ)$ of invertible matrices of rank $2n$ over $R$ which are symplectic with respect to $χ$ acts on the right on the set $Um_{2n}(R)$ of unimodular rows of length $2n$ over $R$. In this paper, we prove that $Sp(χ)$ acts transitively on $Um_{2n}(R)$ if $k$ is algebraically closed, $d! \in k^{\times}$ and $2n \geq d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_06669 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Symplectic orbits of unimodular rows Syed, Tariq Algebraic Geometry K-Theory and Homology For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $χ$ of rank $2n$, the group $Sp(χ)$ of invertible matrices of rank $2n$ over $R$ which are symplectic with respect to $χ$ acts on the right on the set $Um_{2n}(R)$ of unimodular rows of length $2n$ over $R$. In this paper, we prove that $Sp(χ)$ acts transitively on $Um_{2n}(R)$ if $k$ is algebraically closed, $d! \in k^{\times}$ and $2n \geq d$. |
| title | Symplectic orbits of unimodular rows |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2010.06669 |