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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On two-dimensional normal singularities of type $ {}\sb\ast A\sb{n}$, $ {}\sb\ast D\sb{n}$ and $ {}\sb\ast E\sb{n}$


Author: Shigeki Ohyanagi
Journal: Trans. Amer. Math. Soc. 266 (1981), 57-69
MSC: Primary 32C45; Secondary 14J17
DOI: https://doi.org/10.1090/S0002-9947-1981-0613785-9
MathSciNet review: 613785
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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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DOI: https://doi.org/10.1090/S0002-9947-1981-0613785-9
Keywords: Resolution of singularities, weighted dual graph, rational singularity, elliptic singularity
Article copyright: © Copyright 1981 American Mathematical Society