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$A_1$ Du Val singularity and blow ups
Blowing up $\operatorname{Spec}K[x,y]=\mathbb{A}^2$ along $\operatorname{Spec}K[x,y]/(x^2,y)$ in the $U_B$ chart gives a singular point $U_B=\text{Spec}K[x,y][a]/(ya-x^2)$ at the origin. This ...
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