On the Natanzon-Turaev compactification of the Hurwitz space

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2 Scopus citations


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 languageEnglish (US)
Pages (from-to)613-618
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - 2002


  • Hurwitz space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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