  Let the special linear group $G := SL_{2}$ act regularly on a $Q$-factorial
variety $X$. Consider a maximal torus $T \subset G$ and its normalizer $N
\subset G$. We prove: If $U \subset X$ is a maximal open $N$-invariant subset
admitting a good quotient $U \to U // N$ with a divisorial quotient space, then
the intersection $W(U)$ of all translates $g \dot U$ is open in $X$ and admits
a good quotient $W(U) \to W(U) // G$ with a divisorial quotient space.
Conversely, we obtain that every maximal open $G$-invariant subset $W \subset
X$ admitting a good quotient $W \to W // G$ with a divisorial quotient space is
of the form $W = W(U)$ for some maximal open $N$-invariant $U$ as above.
