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Harbater-Mumford subvarieties of moduli spaces of covers

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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 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.

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  1. Mathématiques, Université de Lille 1, 59655, Villeneuve d'Ascq Cedex, France

    Anna Cadoret

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  1. Anna Cadoret
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Cadoret, A. Harbater-Mumford subvarieties of moduli spaces of covers. Math. Ann. 333, 355–391 (2005). https://doi.org/10.1007/s00208-005-0680-0

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