On models of algebraic group actions

TL;DR

This paper proves that any smooth algebraic group action on a variety can be extended to a normal projective model, providing new proofs for foundational results in algebraic transformation groups.

Contribution

It introduces a method to construct normal projective models for smooth algebraic group actions and offers new proofs of classical theorems like Weil's regularization theorem.

Findings

Every smooth algebraic group action admits a normal projective model.

New proofs of key results in algebraic transformation groups.

Enhanced understanding of the structure of algebraic group actions.

Abstract

We show that every action of a smooth algebraic group on a variety admits a normal projective model. Along the way, we present new proofs of some basic results on algebraic transformation groups, including Weil's regularization theorem.