منابع مشابه
2 9 Se p 20 06 Real Belyi Theory
Belyi’s Theorem [Be] of 1979 had a profound effect on Galois Theory, Riemann surfaces and complex algebraic curves. It led Grothendieck [Gr] to develop his theory of dessins d’enfants in which there has been a great interest. The theory is about embedding graphs into compact Riemann surfaces. For further applications to topics such as such as moduli spaces and Physics the reader is recommended ...
متن کاملSeparated Belyi Maps
We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q, and any disjoint finite subsets S, T ⊂ C(Q), we construct a finite morphism φ : C → P such that φ ramifies at each point in S, the branch locus of φ is {0, 1,∞}, and φ(T ) ∩ {0, 1,∞} = ∅. This refines a result of Mochizuki’s. We also prove an analogous result over fields of p...
متن کاملNoncritical Belyi Maps
×ØÖÖغ In the present paper, we present a slightly strengthened version of a well-known theorem of Belyi on the existence of " Belyi maps ". Roughly speaking, this strengthened version asserts that there exist Belyi maps which are unramified at [cf. Theorem 2.5] — or even near [cf. Corollary 3.2] — a prescribed finite set of points. Write C for the complex number field; Q ⊆ C for the subfield o...
متن کاملBelyi functions for Archimedean solids
Without doubt the authentic type of these gures exists in the mind of God the Creator and shares His eternity. Abstract The notion of a Belyi function is a main technical tool which relates the combinatorics of maps (i.e., graphs embedded into surfaces) with Galois theory, algebraic number theory, and the theory of Riemann surfaces. In this paper we compute Belyi functions for a class of semi-r...
متن کاملAn Introduction to Belyi Surfaces
We outline the basic theory of Belyi surfaces, up to Belyi’s theorem (1979, [1]), which characterizes these spaces as precisely those Riemann surfaces that are defined over Q. We then detail the Brooks-Makover construction of a Belyi surface from an oriented cubic graph from [3]. Consequently, we can apply the model of Bollobás in order to randomly pick a Belyi surface. Finally, we briefly expl...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2007
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/ham017