English

On the Belyi degree of a number field

Number Theory 2007-05-23 v1 Algebraic Geometry

Abstract

In this short note we introduce the Belyi degree of a number field K, which is the smallest degree of a dessin d'enfant having K as field of moduli. After the description of some general properties (for example, the fact that there exist finitely many number fields of bounded Belyi degree), we give a lower and an upper bound for such an invariant. We finally give some explicit examples for quadratic fields.

Keywords

Cite

@article{arxiv.math/0611135,
  title  = {On the Belyi degree of a number field},
  author = {Leonardo Zapponi},
  journal= {arXiv preprint arXiv:math/0611135},
  year   = {2007}
}