On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909797407784960 |
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| author | Maguire, Stephen |
| author_facet | Maguire, Stephen |
| contents | This paper is a generalization of a previous paper by the author to connected unipotent linear algebraic groups. The notion of an $ α$-pair answers when an open $ G $-stable, affine, sub-variety $ D(H) $ is a trivial bundle over $ G \backslash \backslash D(H) $ in the Zariski topology, or whether there is an fppf topology $ ϕ: U \to D(H) $ such that $ U $ is a trivial bundle over $ G \backslash \backslash U $ and such that the fibres $ ϕ^{-1}(x) \cong \ker(α) $. We also describe a generalization of van den Essen's algorithm for quasi-principle $ G $-varieties $ \operatorname{Spec}(A) $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective Maguire, Stephen Algebraic Geometry 14D24 This paper is a generalization of a previous paper by the author to connected unipotent linear algebraic groups. The notion of an $ α$-pair answers when an open $ G $-stable, affine, sub-variety $ D(H) $ is a trivial bundle over $ G \backslash \backslash D(H) $ in the Zariski topology, or whether there is an fppf topology $ ϕ: U \to D(H) $ such that $ U $ is a trivial bundle over $ G \backslash \backslash U $ and such that the fibres $ ϕ^{-1}(x) \cong \ker(α) $. We also describe a generalization of van den Essen's algorithm for quasi-principle $ G $-varieties $ \operatorname{Spec}(A) $. |
| title | On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective |
| topic | Algebraic Geometry 14D24 |
| url | https://arxiv.org/abs/2509.15445 |