Hurwitz number fields

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The canonical covering maps from Hurwitz varieties to configuration varieties are important in algebraic geometry. The schemetheoretic fiber above a rational point is commonly connected, in which case it is the spectrum of a Hurwitz number field. We study many examples of such maps and their fibers, finding number fields whose existence contradicts standard mass heuristics.

Original languageEnglish (US)
Pages (from-to)227-272
Number of pages46
JournalNew York Journal of Mathematics
StatePublished - Mar 2 2017

Bibliographical note

Funding Information:
This work was partially supported by the Simons Foundation through grant #209472 and, in its final stages, by the National Science Foundation, through grant DMS-1601350.


  • Discriminant
  • Hurwitz number field
  • Number field
  • Ramification


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