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On rational functions whose normalization has genus zero or one

Volume 182 / 2018

Fedor Pakovich Acta Arithmetica 182 (2018), 73-100 MSC: Primary 14H45, 14H30; Secondary 14G05. DOI: 10.4064/aa170113-28-8 Published online: 14 December 2017

Abstract

We give a complete list of rational functions $A$ such that the genus $g$ of the Galois closure of $\mathbb C(z)/\mathbb C(A)$ equals zero. We also provide a geometric description of those $A$ for which $g=1.$

Authors

  • Fedor PakovichDepartment of Mathematics
    Ben Gurion University
    P.O.B. 653
    Beer Sheva, 8410501, Israel
    e-mail

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