Titlebook: Dessins d‘Enfants on Riemann Surfaces; Gareth A. Jones,Jürgen Wolfart Book 2016 Springer International Publishing Switzerland 2016 Dessins

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dysphagia

Dessins and Triangle Groupsa dessin as a graph embedded in a compact oriented surface leads to a unique conformal structure on this surface, so that the dessin corresponds to a Belyĭ function on the resulting Riemann surface. This shows that our previous definitions of dessins (via Belyĭ functions, embedded graphs or permutat

清醒

懒惰人民

Quasiplatonic Surfaces, and Automorphismsrts, the curves with trivial automorphism group, quasiplatonic curves can be defined over their field of moduli. Many of the automorphism groups appearing in this chapter are 2-dimensional linear or projective groups over finite fields, so we summarise their most relevant properties in the final sec

allergen

Regular Embeddings of Complete Graphsley graphs for the additive groups of finite fields. We enumerate such maps, and show that their automorphism groups are 1-dimensional affine groups. We also show how these maps are related to cyclotomic polynomials, and to primitive polynomials over finite fields.

Foreknowledge

Foreknowledge

Beauville Surfacesion we discuss topological invariants of a Beauville surface, such as its Euler characteristic, fundamental group and automorphism group, and their behaviour under Galois actions. We consider conditions under which a Beauville surface has a real model, and we give examples of Serre’s observation tha

Congestion

1439-7382 , such as the abc conjecture, complex multiplication and Beauville surfaces..Dessins d‘Enfants on Riemann Surfaces. will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic..978-3-319-79664-2978-3-319-24711-3Series ISSN 1439-7382 Series E-ISSN 2196-9922

spinal-stenosis

L. Infante,Steffen Mieske,M. Hilkeron the existence of meromorphic functions with specific properties. In the final section we define Belyĭ functions and prove one direction of Belyĭ’s theorem, that such functions characterise algebraic curves defined over number fields, by using an algorithm which constructs a Belyĭ function on such

推崇

The Evolution of Brightest Cluster Galaxiesa dessin as a graph embedded in a compact oriented surface leads to a unique conformal structure on this surface, so that the dessin corresponds to a Belyĭ function on the resulting Riemann surface. This shows that our previous definitions of dessins (via Belyĭ functions, embedded graphs or permutat