On rational functions whose normalization has genus zero or one
Volume 182 / 2018
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 $g=1.$
