Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908780184207360 |
|---|---|
| author | Shimoji, Taito |
| author_facet | Shimoji, Taito |
| contents | Let $Γ$ be a lattice in a simply-connected nilpotent Lie group $N$ whose Lie algebra $\mathfrak{n}$ is
$p$-filiform. We show that $Γ$ is either abelian or 2-step nilpotent if $Γ$ is isomorphic to the fundamental
group of a smooth complex algebraic variety. Moreover as an application of our result, we give a
required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or
equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties Shimoji, Taito Differential Geometry Algebraic Geometry Algebraic Topology Group Theory Let $Γ$ be a lattice in a simply-connected nilpotent Lie group $N$ whose Lie algebra $\mathfrak{n}$ is $p$-filiform. We show that $Γ$ is either abelian or 2-step nilpotent if $Γ$ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety. |
| title | Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties |
| topic | Differential Geometry Algebraic Geometry Algebraic Topology Group Theory |
| url | https://arxiv.org/abs/2504.08571 |