We compute the number of (weak) equivalence classes of branched covers from a surface of genus g to the sphere, with 3 branching points, degree 2k, and local degrees over the branching points of the form (2,…,2), (2h+1,1,2,…,2), π=dii=1ℓ, for several values of g and h. We obtain explicit formulae of arithmetic nature in terms of the local degrees di. Our proofs employ a combinatorial method based on Grothendieck's dessins d'enfant.

Explicit computation of some families of Hurwitz numbers

Petronio, Carlo
2019

Abstract

We compute the number of (weak) equivalence classes of branched covers from a surface of genus g to the sphere, with 3 branching points, degree 2k, and local degrees over the branching points of the form (2,…,2), (2h+1,1,2,…,2), π=dii=1ℓ, for several values of g and h. We obtain explicit formulae of arithmetic nature in terms of the local degrees di. Our proofs employ a combinatorial method based on Grothendieck's dessins d'enfant.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/934947
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