Stephen Maguire

collaborators

4 papers

math.AG2026

Unirationality is the same thing as Rational Connectedness in Characteristic Zero

Stephen Maguire

In this paper we prove that unirationality, rational connectedness and rational chain connectedness coincide for smooth projective varieties over a field $k$ of characteristic ze…

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 $I^\pm$ -pair answers when an open $G$ -stable, affi…

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 $I^^{2} : G \to GL (V)$ of a linear algebraic group over a field $k$ is the…

Unirationality is the same thing as Rational Connectedness in Characteristic Zero

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