On actions of connected algebraic groups

TL;DR

This paper extends fundamental theorems about algebraic group actions, providing new structural insights for connected algebraic groups acting on various types of algebraic varieties across different characteristics.

Contribution

It generalizes the theorem of the square and local structure results to broader classes of varieties and characteristics, enhancing understanding of algebraic group actions.

Findings

Extended the theorem of the square to seminormal varieties in characteristic 0.

Established local structure results for actions on arbitrary varieties in positive characteristic.

Provided new tools for analyzing algebraic group actions in algebraic geometry.

Abstract

We obtain a version of the theorem of the square and a local structure result for actions of connected algebraic groups on seminormal varieties in characteristic 0, and arbitrary varieties in positive characteristics.