Explicit computation of some families of Hurwitz numbers, II
| Autor: | Carlo Petronio |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Computation
Surface branched cover Hurwitz number 010102 general mathematics Geometric Topology (math.GT) 0102 computer and information sciences 01 natural sciences Algebra 57M12 Mathematics - Geometric Topology 010201 computation theory & mathematics FOS: Mathematics Geometry and Topology 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1807.11067 |
| Popis: | We continue our computation, using a combinatorial method based on Gronthendieck's dessins d'enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate on data with the surface of genus g as source surface, the sphere as target surface, 3 branching points, degree 2k, and local degrees over the branching points of the form [2,...,2], [2h+1,3,2,...,2], [d_1,...,d_l]. We compute the corresponding (weak) Hurwitz numbers for several values of g and h, getting explicit arithmetic formulae in terms of the d_i's. Comment: 25 pages, 10 figures |
| Databáze: | OpenAIRE |
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