This is close to Balazs's answer. $X$ is the nilpotent cone for $SL(2)$. The Springer resolution $T^* \mathbb P^1 \to X$ is small. $T^* \mathbb P^1$ is the total space of the line bundle $O(-2)$ on $\mathbb P^1$. So global functions on $X$ are the same as global functions on the total space of the bundle $O(-2)$ on $\mathbb P^1$ whose structure sheaf is ${\rm Sym}^* O(-2)^\vee$. See [this](https://math.stackexchange.com/questions/1117282/when-is-the-symmetric-algebra-of-a-vector-bundle-finitely-generated) and [this](https://mathoverflow.net/questions/262721/total-space-of-canonical-bundle-as-resolution-of-singularity) questions.