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This is a Quantitative Study study.

October 2, 2025Open Access

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

Key Points

Open $G$-stable affine sub-varieties can either form trivial bundles or exhibit more complex structures, with implications for topology.
The study introduces an $\alpha$-pair concept that defines specific bundle conditions over $G$-actions in connected unipotent groups.
Generalizations of van den Essen's algorithm are explored for quasi-principle $G$-varieties, contributing to geometric invariant theory.
Connections between Zariski and fppf topologies influence the classification of variations in group actions on varieties.

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 D (H) in the Zariski topology, or whether there is an fppf topology ϕ: U D (H) such that U is a trivial bundle over G U and such that the fibres ϕ^-1 (x) (α). We also describe a generalization of van den Essen's algorithm for quasi-principle G -varieties Spec (A).

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Cite This Study

Stephen Maguire (Thu,) studied this question.

synapsesocial.com/papers/68de5da283cbc991d0a208d8 https://doi.org/https://doi.org/10.48550/arxiv.2509.15445

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