  For $C$ a stable curve of arithmetic genus $g\ge 2$, and $\mathcal{D}$ the
determinant of cohomology line bundle on
$\operatorname{Bun}_{\operatorname{SL}(r)}(C)$, we show the section ring for
the pair $(\operatorname{Bun}_{\operatorname{SL}(r)}(C), \mathcal{D})$ is
finitely generated. Three applications are given.
