Hyperelliptic maps and surfaces. (English) Zbl 0958.05035

The author focuses on the relationship between hyperelliptic maps and hyperelliptic Riemann surfaces. It is known that underlying any map \(M\) on an orientable surface, there is a unique Riemann surface \(X(M)\) naturally associated with \(M\). If \(M\) is hyperelliptic then so is \(X(M)\). It is also shown that in the special case when \(M\) is a regular map, the converse holds.


05C10 Planar graphs; geometric and topological aspects of graph theory
30F99 Riemann surfaces
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