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Mathematische Annalen

, Volume 333, Issue 2, pp 355–391 | Cite as

Harbater-Mumford subvarieties of moduli spaces of covers

  • Anna CadoretEmail author
Article

Abstract

We define Harbater-Mumford subvarieties, which are special kinds of closed subvarieties of Hurwitz moduli spaces obtained by fixing some of the branch points. We show that, for many finite groups, finding geometrically irreducible HM-subvarieties defined over Open image in new window is always possible. This provides information on the arithmetic of Hurwitz spaces and applies in particular to the regular inverse Galois problem with (almost all) fixed branch points. Profinite versions of our results can also be stated, providing new tools to study the geometry of modular towers and the regular inverse Galois problem for profinite groups.

Mathematics Subject Classification (2000)

12F12 14G32 20E45 14H30 20E22 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.MathématiquesVilleneuve d'Ascq CedexFrance

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