## Spherical conic metrics and realizability of branched covers

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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.## References

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## Additional Information

**Xuwen Zhu**- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 1220465
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1805-1815 - MSC (2010): Primary 57M12; Secondary 53C20
- DOI: https://doi.org/10.1090/proc/14318
- MathSciNet review: 3910445