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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Normal two-dimensional elliptic singularities
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by Stephen Shing Toung Yau PDF
Trans. Amer. Math. Soc. 254 (1979), 117-134 Request permission

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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Additional Information
  • © Copyright 1979 American Mathematical Society
  • 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