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On the Natanzon-Turaev compactification of the Hurwitz space

Author(s): Steven P. Diaz
Journal: Proc. Amer. Math. Soc. 130 (2002), 613-618.
MSC (2000): Primary 14H10; Secondary 57M12
Posted: October 23, 2001
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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.

References:

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S. Diaz and D. Edidin, Towards the Homology of Hurwitz Spaces, J. Differential Geometry Vol. 43, No. 1, (1996), 66-98. MR 98e:14028

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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: 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
Posted: October 23, 2001
Communicated by: Michael Stillman
Copyright of article: Copyright 2001, American Mathematical Society

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