Commuting varieties in bad characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908807950499840 |
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| author | Roman, Vlad |
| author_facet | Roman, Vlad |
| contents | Let $k$ be an algebraically closed field of characteristic $2$. We consider the commuting variety and the commuting nilpotent variety of the Lie algebra $\mathfrak{sp}_{2n}$, namely the sets $\mathcal{C}_2(\mathfrak{sp}_{2n})=\{ (x,y) \in \mathfrak{sp}_{2n} \times \mathfrak{sp}_{2n} \mid [x,y]=0\}$ and $\mathcal{C}_2^{\text{nil}}(\mathfrak{sp}_{2n})=\{ (x,y) \in \mathfrak{sp}_{2n} \times \mathfrak{sp}_{2n} \mid x,y \text{ nilpotent, } [x,y]=0\}$ and prove that they are both irreducible, of dimensions $\dim(\mathfrak{sp}_{2n}) + 2n$ and $\dim(\mathfrak{sp}_{2n}) + n-1$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02935 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Commuting varieties in bad characteristic Roman, Vlad Algebraic Geometry Rings and Algebras Representation Theory Let $k$ be an algebraically closed field of characteristic $2$. We consider the commuting variety and the commuting nilpotent variety of the Lie algebra $\mathfrak{sp}_{2n}$, namely the sets $\mathcal{C}_2(\mathfrak{sp}_{2n})=\{ (x,y) \in \mathfrak{sp}_{2n} \times \mathfrak{sp}_{2n} \mid [x,y]=0\}$ and $\mathcal{C}_2^{\text{nil}}(\mathfrak{sp}_{2n})=\{ (x,y) \in \mathfrak{sp}_{2n} \times \mathfrak{sp}_{2n} \mid x,y \text{ nilpotent, } [x,y]=0\}$ and prove that they are both irreducible, of dimensions $\dim(\mathfrak{sp}_{2n}) + 2n$ and $\dim(\mathfrak{sp}_{2n}) + n-1$, respectively. |
| title | Commuting varieties in bad characteristic |
| topic | Algebraic Geometry Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2602.02935 |