2019/07/24 by Ruben A. Hidalgo, Hidalgo, Ruben A. · 1 citation
Mathematics · #14H30 #30F40 #32G15 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:14H30 #msc:30F40 #msc:32G15
paper · pdf · doi:10.48550/arxiv.1907.10692
arxiv created 2019/07/24 · arxiv updated 2019/07/26
A closed Riemann surface S (of genus at least one) is called an origami curve if it admits a non-constant holomorphic map β:S → E with at most one branch value, where E is a genus one Riemann surface. In this case, (S,β) is called an origami pair and \rm Aut(S,β) is the group of conformal automorphisms ϕ of S such that β=β∘ ϕ. Let G be a finite group. It is a known fact that G can be realized as a subgroup of \rm Aut(S,β) for a suitable origami pair (S,β). It is also known that G can be realized as a group of conformal automorphisms of a Riemann surface X of genus g ≥ 2 and with quotient orbifold X/G also of genus γ≥ 2. Given a conformal action of G on a surface X as before, we prove that there is an origami pair (S,β), where S has genus g and G ≅ \rm Aut(S,β) such that the actions of \rm Aut(S,β) on S and that of G on X are topologically equivalent.