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The Milnor Fiber Conjecture and iterated branched cyclic covers


Author: P. J. Lamberson
Journal: Trans. Amer. Math. Soc. 361 (2009), 4653-4681
MSC (2000): Primary 14B05, 32S55; Secondary 32S25, 32S50, 57M12, 57N10
DOI: https://doi.org/10.1090/S0002-9947-09-04647-9
Published electronically: April 15, 2009
MathSciNet review: 2506423
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Abstract: In this paper we prove the Milnor Fiber Conjecture of Neumann and Wahl for a class of isolated complete intersection singularities obtained by taking iterated branched cyclic covers of the singularity link. We also show that if the Milnor Fiber Conjecture holds for a given splice diagram, then it holds for any equivalent diagram satisfying the semigroup condition. We illustrate the application of these theorems in an example and discuss the relationship of these singularities with Neumann and Wahl's Splice Type Conjecture.


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Additional Information

P. J. Lamberson
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Address at time of publication: Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109
Email: pjlamber@umich.edu

DOI: https://doi.org/10.1090/S0002-9947-09-04647-9
Received by editor(s): June 25, 2007
Published electronically: April 15, 2009
Additional Notes: This work was carried out while the author was a Ph.D. student at Columbia University, supported by a graduate fellowship. Part of this research was completed while the author was supported by the Carl B. Boyer Memorial Fellowship. The author wishes to thank Walter Neumann for invaluable guidance in conducting this research.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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