Harbater-Mumford subvarieties of moduli spaces of covers
Harbater-Mumford subvarieties of moduli spaces of covers
复制标题
覆盖模空间的 Harbater-Mumford 子变体
DOI：
10.1007/s00208-005-0680-0
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发表时间：
2005
影响因子：
1.4
通讯作者：
A. Cadoret
中科院分区：
文献类型：
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作者：
A. Cadoret
定义了Harbater-Mumford子簇，它是Hurwitz模空间的一类特殊的闭子簇，通过固定某些分支点而得到.我们证明，对于许多有限群，找到定义在上的几何不可约HM-子簇， 总是有可能的。这提供了信息的算术赫维茨空间，特别适用于经常逆伽罗瓦问题（几乎所有）固定分支点。我们的结果的Profinite版本也可以说，提供了新的工具来研究几何的模块塔和定期逆伽罗瓦问题profinite群。
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.