Search results for "Monodromy groups"

MR 3215343 Reviewed Pirola G.P., Rizzi C. and Schlesinger E. A new curve algebraically but not rationally uniformized by radicals. Asian J. Math., 18…

2014

A smooth projective complex curve C is called rationally uniformized by radicals if there exists a covering map C \rightarrow P^1 with solvable Galois group. C is called algebraically uniformized by radicals if there exists a finite covering C^{\prime} \rightarrow C with C^{\prime} rationally uniformized by radicals. Abramovich and Harris posed the following problem in [D. Abramovich and J. Harris, Abelian varieties and curves in $W_{d}(C)$, Compositio Math., 78 (1991), pp. 227–-238]. \vspace{1ex} Statement S(d, h, g): \textit{Suppose C^{\prime} \rightarrow C is a nonconstant map of smooth curves with C of genus g. If C^{\prime} admits a map of degree d or less to a curve of genus h or less…