On the Natanzon-Turaev compactification of the Hurwitz space

Steven P. Diaz

doi:10.1090/S0002-9939-01-06393-6

On the Natanzon-Turaev compactification of the Hurwitz space

Steven P. Diaz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	613-618
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	130
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-01-06393-6
State	Published - 2002

Keywords

Hurwitz space

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-01-06393-6

Cite this

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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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AB - 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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On the Natanzon-Turaev compactification of the Hurwitz space

Abstract

Keywords

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