Classification of affine normal $SL_2$-varieties with a dense orbit

TL;DR

This paper offers an alternative classification of affine normal $SL_2$-varieties with a dense orbit, expanding on Popov's earlier work by providing a new method.

Contribution

It presents a novel approach to classifying affine normal $SL_2$-varieties with a dense orbit, differing from previous methods.

Findings

Complete classification of affine normal $SL_2$-varieties with a dense orbit

Alternative proof to Popov's classification

New insights into the structure of these varieties

Abstract

In this note we give a classification of all affine normal $SL_2$-varieties containing an open dense orbit over an algebraically closed field of characteristic zero. Such a classification was first obtained by Popov. Here we provide an alternative approach.