Sorry if this question is a bit broad. I would like to have examples of papers which have studied the surface singularity
$$x^4=yz,\quad(x,y,z\in\mathbb{C}).$$
I am trying to get a feel about what is known about it in the literature.



The surface singularity $x^4=yz$
This singularity, and more generally the ones given by $x^n + yz=0$ are (well-)known as an ADE singularity. The ring $C[x,y,z] / x^n + yz$ is the ring of coordinates of the quotient of the natural $\mathbf Z/n \subset SL\_2(\mathbf C)$-action on $\mathbf C^2$. Check out some literature on the McKay-correspondence for further information.


