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.
Autori interni: | ||
Autori: | Petronio, Carlo | |
Titolo: | Explicit computation of some families of Hurwitz numbers | |
Anno del prodotto: | 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. | |
Digital Object Identifier (DOI): | 10.1016/j.ejc.2018.08.008 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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