Abstract:We prove that there exists no branched cover from the torus to the sphere with degree 3h and 3 branching points in the target with local degrees (3, . . . , 3), (3, . . . , 3), (4, 2, 3, . . . , 3) at their preimages. The result was already established by Izmestiev, Kusner, Rote, Springborn, and Sullivan, using geometric techniques, and by Corvaja and Zannier with a more algebraic approach, whereas our proof is topological and completely elementary: besides the definitions, it only uses the fact that on the to… Show more
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