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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 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 -pair answers when an open -stable, affin…

math.AG2025

On the Invariant Theory of -Actions from a Geometric Perspective

Stephen Maguire

In this paper we give a strict classification of -representations. This is done through the notion of a -pair. Namely if is a $…

math.AG2025

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

Stephen Maguire

Hilbert's 14th Problem asks the following question. Given a linear representation of a linear algebraic group over a field is the r…

math.AG2024

Unirationality is the Same as Rational Connectedness in Characteristic Zero

Stephen Maguire

In this paper we describe a fibration for a smooth, projective variety over a field of characteristic zero. This fibration is similar to the MRC fibration, and we call it the…