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Spherical conic metrics and realizability of branched covers


Author: Xuwen Zhu
Journal: Proc. Amer. Math. Soc. 147 (2019), 1805-1815
MSC (2010): Primary 57M12; Secondary 53C20
DOI: https://doi.org/10.1090/proc/14318
Published electronically: December 6, 2018
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Abstract: Branched covers between Riemann surfaces are associated with certain combinatorial data, and the Hurwitz existence problem asks whether given data, satisfying those combinatorial constraints can be realized by some branched cover. We connect recent developments in spherical conic metrics to this old problem and give a new method of finding exceptional (unrealizable) branching data. As an application, we find new infinite sets of exceptional branched cover data on the Riemann sphere.


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Xuwen Zhu
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

DOI: https://doi.org/10.1090/proc/14318
Received by editor(s): June 4, 2018
Received by editor(s) in revised form: July 14, 2018
Published electronically: December 6, 2018
Communicated by: Guofang Wei
Article copyright: © Copyright 2018 American Mathematical Society