Harbater-Mumford subvarieties of moduli spaces of covers
Language
en
Article de revue
This item was published in
Mathematical annalen. 2005, vol. 333, n° 2, p. 355-391
English Abstract
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- ...Read more >
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.Read less <
Origin
Hal imported