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ℤ/rℤ-equivariant covers of ℙ1 with moving ramification

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Abstract

Let X → ℙ1 be a general cyclic cover. We give a simple formula for the number of equivariant meromorphic functions on X subject to ramification conditions at variable points. This generalizes and gives a new proof of a recent result of the second author and Pirola on hyperelliptic odd covers.

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Acknowledgments

C.L. was supported by an NSF Postdoctoral Fellowship, grant DMS-2001976. R.M. was supported by MIUR: Dipartimenti di Eccellenza Program (2018–2022)-Dept. of Math. Univ. of Pavia and by PRIN Project Moduli spaces and Lie theory (2017). We thank Gavril Farkas, Pietro Pirola and Johannes Schmitt for helpful comments and correspondence.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, 12489, Berlin, Germany

    Carl Lian

  2. Department of Mathematics G. Peano, University of Turin, via Carlo Alberto 10, 10123, Torino, Italy

    Riccardo Moschetti

Authors
  1. Carl Lian
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  2. Riccardo Moschetti
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Correspondence to Carl Lian.

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Lian, C., Moschetti, R. ℤ/rℤ-equivariant covers of ℙ1 with moving ramification. Isr. J. Math. 253, 487–500 (2023). https://doi.org/10.1007/s11856-022-2387-2

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  • DOI: https://doi.org/10.1007/s11856-022-2387-2

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