The lift invariant distinguishes components of Hurwitz spaces for 𝐴₅

James, Adam; Magaard, Kay; Shpectorov, Sergey

doi:10.1090/S0002-9939-2014-12185-X

The lift invariant distinguishes components of Hurwitz spaces for $A_5$
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by Adam James, Kay Magaard and Sergey Shpectorov PDF

Proc. Amer. Math. Soc. 143 (2015), 1377-1390 Request permission

Abstract:

Hurwitz spaces are moduli spaces of curve covers. The isomorphism classes of covers of ${P}^1\mathbb {C}$ with given ramification data are parameterized combinatorially by Nielsen tuples in the monodromy group $G$. The Artin braid group acts on Nielsen tuples, and the orbits of this action correspond to the connected components of the corresponding Hurwitz space. In this article we consider the case $G=A_5$. We give a complete classification of the braid orbits for all ramification types, showing that the components are always distinguishable by the Fried-Serre lift invariant.

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