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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Natanzon-Turaev compactification of the Hurwitz space


Author: Steven P. Diaz
Journal: Proc. Amer. Math. Soc. 130 (2002), 613-618
MSC (2000): Primary 14H10; Secondary 57M12
Published electronically: October 23, 2001
MathSciNet review: 1866008
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Abstract: Natanzon and Turaev have constructed by topological methods a compactification of the Hurwitz space, that is, the space of simple branched covers of the two-sphere. Here we show that this compactification is homeomorphic to a compactification mentioned by Diaz and Edidin (in 1996) that was constructed by algebraic methods. Using this we are able to show by example that the Natanzon-Turaev compactification can be singular, that is, not a manifold.


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Additional Information

Steven P. Diaz
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email: spdiaz@mailbox.syr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06393-6
PII: S 0002-9939(01)06393-6
Keywords: Hurwitz space
Received by editor(s): August 17, 1999
Received by editor(s) in revised form: March 8, 2000
Published electronically: October 23, 2001
Communicated by: Michael Stillman
Article copyright: © Copyright 2001 American Mathematical Society