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The lift invariant distinguishes components of Hurwitz spaces for $ A_5$


Authors: Adam James, Kay Magaard and Sergey Shpectorov
Journal: Proc. Amer. Math. Soc. 143 (2015), 1377-1390
MSC (2010): Primary 20B25, 20B40; Secondary 14H55, 20F36, 14H10
DOI: https://doi.org/10.1090/S0002-9939-2014-12185-X
Published electronically: December 3, 2014
MathSciNet review: 3314053
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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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Additional Information

Adam James
Affiliation: School of Mathematics, University of Birmingham, Birmingham, B15 2TT, United Kingdom
Email: adamjames87@gmail.com

Kay Magaard
Affiliation: School of Mathematics, University of Birmingham, Birmingham, B15 2TT, United Kingdom
Email: k.magaard@bham.ac.uk

Sergey Shpectorov
Affiliation: School of Mathematics, University of Birmingham, Birmingham, B15 2TT, United Kingdom
Email: S.Shpectorov@bham.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2014-12185-X
Received by editor(s): October 12, 2012
Received by editor(s) in revised form: February 25, 2013
Published electronically: December 3, 2014
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.