Harbater-Mumford subvarieties of moduli spaces of covers
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en
Article de revue
Este ítem está publicado en
Mathematical annalen. 2005, vol. 333, n° 2, p. 355-391
Resumen en inglés
In this paper 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 geomet- ...Leer más >
In this paper 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 geomet- rically irreducible HM-subvarieties defined over Q 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.< Leer menos
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