Pairs of tree dessins, their Shabat polynomials, and monodromy groups
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912642696740864 |
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| author | Dupont, Benjamin Kyriakoglou, Revekka Metaftsis, Vassilis Prassidis, Efstratios Singh, Alexandros |
| author_facet | Dupont, Benjamin Kyriakoglou, Revekka Metaftsis, Vassilis Prassidis, Efstratios Singh, Alexandros |
| contents | Coverings of the Riemann sphere by itself, ramified over two points, are given by so-called Shabat polynomials. The correspondence between Grothendieck's dessins d'enfants and Belyi maps then implies a bijection between Shabat polynomials and tree dessins (bicolored plane trees). Dessins can be assigned a combinatorial invariant known as their passport, which records the degrees of their vertices. We consider all possible passports determining a pair of tree dessins, determining the associated Shabat polynomials and monodromy groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pairs of tree dessins, their Shabat polynomials, and monodromy groups Dupont, Benjamin Kyriakoglou, Revekka Metaftsis, Vassilis Prassidis, Efstratios Singh, Alexandros Algebraic Geometry Combinatorics Group Theory 14H57 Coverings of the Riemann sphere by itself, ramified over two points, are given by so-called Shabat polynomials. The correspondence between Grothendieck's dessins d'enfants and Belyi maps then implies a bijection between Shabat polynomials and tree dessins (bicolored plane trees). Dessins can be assigned a combinatorial invariant known as their passport, which records the degrees of their vertices. We consider all possible passports determining a pair of tree dessins, determining the associated Shabat polynomials and monodromy groups. |
| title | Pairs of tree dessins, their Shabat polynomials, and monodromy groups |
| topic | Algebraic Geometry Combinatorics Group Theory 14H57 |
| url | https://arxiv.org/abs/2510.10192 |