The variety of nilpotent pairs $(A,B)$ with $[A,B] = λI$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910006414147584 |
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| author | Roman, Vlad Guralnick, Robert M. |
| author_facet | Roman, Vlad Guralnick, Robert M. |
| contents | Let $k$ be an algebraically closed field of characteristic $p >0$. We consider the variety of nilpotent pairs $(A,B)$ with $[A,B]=λI$, namely the set of pairs $ X = \{ (A,B) \in M_n(k) \times M_n(k) \mid A,B \text{ nilpotent}, [A,B]=λI, λ\in k \}$. We prove that if $n=pr$, then $X$ is irreducible of dimension $n^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The variety of nilpotent pairs $(A,B)$ with $[A,B] = λI$ Roman, Vlad Guralnick, Robert M. Algebraic Geometry Let $k$ be an algebraically closed field of characteristic $p >0$. We consider the variety of nilpotent pairs $(A,B)$ with $[A,B]=λI$, namely the set of pairs $ X = \{ (A,B) \in M_n(k) \times M_n(k) \mid A,B \text{ nilpotent}, [A,B]=λI, λ\in k \}$. We prove that if $n=pr$, then $X$ is irreducible of dimension $n^2$. |
| title | The variety of nilpotent pairs $(A,B)$ with $[A,B] = λI$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.20199 |