On the existence of covers of $\mathbb P_1$ associated to certain permutations
Pietro Corvaja, Umberto M. Zannier · Rendiconti Lincei Matematica e Applicazioni · 2018
In this short note we prove the impossibility of realizing finite topological covers of the Riemann sphere minus three points, associated to certain explicit combinatorial (permutation) data. This comes from a question of M. Zieve and falls in the framework of the so-called ‘‘Hurwitz problem’’, asking for a ‘‘simple’’ description of the combinatorial data which can be so realized.