Galois actions on regular dessins of small genera | Zendy

Marston Conder | Zendy; Gareth A. Jones | Zendy; Manfred Streit | Zendy; Jürgen Wolfart | Zendy

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Galois actions on regular dessins of small genera

Author(s) -

Marston Conder,

Gareth A. Jones,

Manfred Streit,

Jürgen Wolfart

Publication year - 2013

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/717

Subject(s) - mathematics , algebraic curve , genus , galois theory , bipartite graph , automorphism group , automorphism , transitive relation , group (periodic table) , field (mathematics) , pure mathematics , enhanced data rates for gsm evolution , surface (topology) , combinatorics , geometry , computer science , physics , graph , botany , biology , telecommunications , quantum mechanics

Dessins d'enfants can be regarded as bipartite graphs embed- ded in compact orientable surfaces. According to Grothendieck and others, a dessin uniquely determines a complex structure on the surface, and even an algebraic structure (as a projective algebraic curve dened over a num- ber eld). The general problem of how to determine all properties of the curve from the combinatorics of the dessin is far from being solved. For regular dessins, which are those having an edge{transitive automorphism group, the situation is easier: currently available methods in combinatorial and computational group theory allow the determination of the elds of denition for all curves with regular dessins of genus 2 to 18.

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