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Transactions of the American Mathematical Society

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Normal two-dimensional elliptic singularities


Author: Stephen Shing Toung Yau
Journal: Trans. Amer. Math. Soc. 254 (1979), 117-134
MSC: Primary 32C40
DOI: https://doi.org/10.1090/S0002-9947-1979-0539910-7
MathSciNet review: 539910
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Abstract: Given a weighted dual graph such that the canonical cycle $ K'$ exists, is there a singularity corresponding to the given weighted dual graph and which has Gorenstein structure? This is one of the important problems in normal surface singularities. In this paper, we give a necessary and sufficient condition for the existence of Gorenstein structures for weakly elliptic singularities. A necessary and sufficient condition for the existence of maximally elliptic structure is also given. Hence, the above question is answered affirmatively for a special kind of singularities. We also develop a theory for those elliptic Gorenstein singularities with geometric genus equal to three.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0539910-7
Article copyright: © Copyright 1979 American Mathematical Society

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