On ovals of Riemann surfaces of even genera
Using NEC groups and combinatorial methods, the authors show that three nonconjugate symmetries of a surface of even genus \(g\) have at most \(2g+3\) ovals. Besides this they show that if such a surface admits four nonconjugate symmetries then its total number of ovals does not exceed \(2g+2\). Also they prove that, for every even genus \(g\) and for surfaces with automorphism group \(D_n\times\mathbb{Z}_2\) (each \(n\) dividing \(2g\)), this bound is sharp.
scientific article; zbMATH DE number 1383257