Monodromy groups of Hurwitz-type problems

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• 作者：Daniel Allcock ; Chris Hall
• 关键词：Hurwitz space ; Monodromy ; Simply branched covers
• 刊名：Advances in Mathematics
• 出版年：2010
• 出版时间：10 September 2010
• 年：2010
• 卷：225
• 期：1
• 页码：69-80
• 全文大小：190 K

文摘

We solve the Hurwitz monodromy problem for degree 4 covers. That is, the Hurwitz space of all simply branched covers of of degree 4 and genus g is an unramified cover of the space of (2g+6)-tuples of distinct points in . We determine the monodromy of on the points of the fiber. This turns out to be the same problem as the action of on a certain local system of -vector spaces. We generalize our result by treating the analogous local system with coefficients, 3N, in place of . This in turn allows us to answer a question of Ellenberg concerning families of Galois covers of with deck group .