Stephen Maguire

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20242026

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math.AG2025

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

Stephen Maguire

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, affin…

math.AG2025

On the Invariant Theory of $G_{a}$ -Actions from a Geometric Perspective

Stephen Maguire

In this paper we give a strict classification of $G_{a}$ -representations. This is done through the notion of a $c (t)$ -pair. Namely if $Spec (A)$ is a $…

math.AG2025

Invariant Rings of $G_{a}$ -Representations are not always Finitely Generated in Positive Characteristic

Stephen Maguire

Hilbert's 14th Problem asks the following question. Given a linear representation $β : G \to GL (V)$ of a linear algebraic group over a field $k$ is the r…

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

On the Invariant Theory of Ga​-Actions from a Geometric Perspective

Invariant Rings of Ga​-Representations are not always Finitely Generated in Positive Characteristic

On the Invariant Theory of $G_{a}$ -Actions from a Geometric Perspective

Invariant Rings of $G_{a}$ -Representations are not always Finitely Generated in Positive Characteristic