Abstract
In this paper, we define tropical analogues of real Hurwitz numbers, i.e. numbers of covers of surfaces with compatible involutions satisfying prescribed ramification properties. We prove a correspondence theorem stating the equality of the tropical numbers with their real counterparts. We apply this theorem to the case of double Hurwitz numbers [which generalizes our result from Guay-Paquet et al. (2014)].
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Acknowledgments
The first author is supported by DFG-Grant MA 4797/1-2 and GIF Grant No. 1174-197.6/2011. The second author would like to thank the Université de Genève for the hospitality during his stay. We would like to thank Erwan Brugallé, Ilia Itenberg and Grisha Mikhalkin for helpful discussions. We also thank Maxim Karev and an anonymous referee for helpful remarks on earlier versions of this paper.
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Markwig, H., Rau, J. Tropical real Hurwitz numbers. Math. Z. 281, 501–522 (2015). https://doi.org/10.1007/s00209-015-1498-4
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DOI: https://doi.org/10.1007/s00209-015-1498-4