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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classification of weighted dual graphs with only complete intersection singularities structures


Authors: Fan Chung, Yi-Jing Xu and Stephen S.-T. Yau
Journal: Trans. Amer. Math. Soc. 361 (2009), 3535-3596
MSC (2000): Primary 32S25, 58K65, 14B05
Published electronically: March 4, 2009
MathSciNet review: 2491891
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Abstract: Let $ p$ be normal singularity of the 2-dimensional Stein space $ V$. Let $ \pi\colon M\to V$ be a minimal good resolution of $ V$, such that the irreducible components $ A_i$ of $ A=\pi^{-1}(p)$ are nonsingular and have only normal crossings. Associated to $ A$ is weighted dual graph $ \Gamma$ which, along with the genera of the $ A_i$, fully describes the topology and differentiable structure of $ A$ and the topological and differentiable nature of the embedding of $ A$ in $ M$. In this paper we give the complete classification of weighted dual graphs which have only complete intersection singularities but no hypersurface singularities associated to them. We also give the complete classification of weighted dual graphs which have only complete intersection singularities associated with them.


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Additional Information

Fan Chung
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112

Yi-Jing Xu
Affiliation: Department of Mathematics, John Tyler Community College, 13101 Jefferson Davis Highway, Chester, Virginia 23831-5316

Stephen S.-T. Yau
Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045
Email: yau@uic.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04524-3
PII: S 0002-9947(09)04524-3
Received by editor(s): March 2, 2007
Published electronically: March 4, 2009
Additional Notes: The third author’s research was partially supported by an NSF grant.
Dedicated: Dedicated to Henry Laufer on the occasion of his 65th birthday
Article copyright: © Copyright 2009 American Mathematical Society