Abstract
We study the real counterpart of double Hurwitz numbers, called real double Hurwitz numbers here. We establish a lower bound for these numbers with respect to their dependence on the distribution of branch points. We use it to prove, under certain conditions, existence of real Hurwitz covers as well as logarithmic equivalence of real and classical Hurwitz numbers. The lower bound is based on the “tropical” computation of real Hurwitz numbers in Markwig and Rau (Math Z 281(1–2):501–522, 2015).
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Acknowledgements
The author would like to thank Renzo Cavalieri, Boulos El Hilany, Ilia Itenberg, Maksim Karev, Lionel Lang and Hannah Markwig for helpful discussions. Parts of this work were carried out at Institut Mittag-Leffler during my visit of the research program “Tropical Geometry, Amoebas and Polytopes”. Many thanks for the great hospitality and atmosphere!
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Communicated by Jean-Yves Welschinger.
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For this work, the author was supported by the DFG Research Grant RA 2638/2-1.
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Rau, J. Lower bounds and asymptotics of real double Hurwitz numbers. Math. Ann. 375, 895–915 (2019). https://doi.org/10.1007/s00208-019-01863-y
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DOI: https://doi.org/10.1007/s00208-019-01863-y