Zeige explizit, dass der Ring C [ X , Y , Z ] / ( X 2 + Y Z 2 + Y 2 ) {\displaystyle {}{\mathbb {C} }[X,Y,Z]/{\left(X^{2}+YZ^{2}+Y^{2}\right)}} (also die Diedersingularität zu m = 1 {\displaystyle m=1} ) isomorph zu C [ S , T , U ] / ( S T − U 4 ) {\displaystyle {}{\mathbb {C} }[S,T,U]/{\left(ST-U^{4}\right)}} ist.
![{\displaystyle {}{\mathbb {C} }[X,Y,Z]/{\left(X^{2}+YZ^{2}+Y^{2}\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71571164ce71f7a3c97493c50323fca567c46722)
![{\displaystyle {}{\mathbb {C} }[S,T,U]/{\left(ST-U^{4}\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f7c54f3d09e80247c563371a195ae0aebf33ab0e)