Classification of weighted dual graphs with only complete intersection singularities structures
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- by Fan Chung, Yi-Jing Xu and Stephen S.-T. Yau PDF
- Trans. Amer. Math. Soc. 361 (2009), 3535-3596 Request permission
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.References
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Additional Information
- Fan Chung
- Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
- MR Author ID: 49205
- 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
- MR Author ID: 185485
- Email: yau@uic.edu
- 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.
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 3535-3596
- MSC (2000): Primary 32S25, 58K65, 14B05
- DOI: https://doi.org/10.1090/S0002-9947-09-04524-3
- MathSciNet review: 2491891
Dedicated: Dedicated to Henry Laufer on the occasion of his 65th birthday