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arXiv · 2509.15445

On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective

Stephen Maguire
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Abstract

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) $.

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Stephen Maguire. 2025-09-18. On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective. https://arxiv.org/abs/2509.15445

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