Moduli spaces and the algebra of conformal blocks

For a classical simple and simply connected group $G$, let $\mathcal{M}_{G,\omega}$ be the moduli space of $\omega$-semistable parabolic $G$-bundles on a complex smooth projective curve of genus $g$. We prove two results in this article: (1) $\mathcal{M}_{G,\omega}$ is of Fano type when $g\geq 3$; (2) the algebra of conformal blocks on any $n$-pointed stable curve for a classical simple Lie algebra is finitely generated.