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.
2
-
4$\begingroup$ This is a du Val singularity of type $A_3$. $\endgroup$– BortCommented Aug 31, 2018 at 13:40
-
$\begingroup$ Indeed, just the same as $x^4 + y^2 + z^2$. $\endgroup$– F. C.Commented Aug 31, 2018 at 19:03
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
0
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.
