Homogeneous varieties under split solvable algebraic groups

TL;DR

This paper provides a modern proof of Rosenlicht's theorem, showing that certain algebraic varieties are isomorphic to products of affine lines and punctured affine lines, clarifying their structure.

Contribution

It offers a new, streamlined proof of a classical result about the structure of homogeneous varieties under split solvable algebraic groups.

Findings

Varieties are isomorphic to products of affine and punctured affine lines

Simplified proof of Rosenlicht's theorem

Enhanced understanding of algebraic group actions on varieties

Abstract

We present a modern proof of a theorem of Rosenlicht, asserting that every variety as in the title is isomorphic to a product of affine lines and punctured affine lines.