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, C.. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - 75:(2019), pp. 136-151. [10.1016/j.ejc.2018.08.008]
Explicit computation of some families of Hurwitz numbers
Petronio C.
2019-01-01
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.File in questo prodotto:
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