On two-dimensional normal singularities of type _{∗}𝐴_{𝑛}, _{∗}𝐷_{𝑛} and _{∗}𝐸_{𝑛}

Ohyanagi, Shigeki

doi:10.1090/S0002-9947-1981-0613785-9

On two-dimensional normal singularities of type ${}_\ast A_{n}$, ${}_\ast D_{n}$ and ${}_\ast E_{n}$
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Trans. Amer. Math. Soc. 266 (1981), 57-69 Request permission

Abstract:

Let $G$ be the weighted dual graph associated with a contractible curve $A = \cup {A_i}$. There are many combinations of the weights ${A_i} \cdot {A_i}$ which make the graph contractible. If $G$ is a graph which is the weighted dual graph for a rational singularity with any combination of the weights, then $G$ is either ${}_ \ast {A_n}$, ${}_ \ast {D_n}$ or $_\ast {E_n}$.

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On two-dimensional normal singularities whose minimal resolutions are of type

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