Polynomial bounds for Arakelov invariants of Belyi curves

@article{Javanpeykar2014PolynomialBF,
  title={Polynomial bounds for Arakelov invariants of Belyi curves},
  author={Ariyan Javanpeykar and Peter Bruin},
  journal={Algebra \& Number Theory},
  year={2014},
  volume={8},
  pages={89-140}
}
We explicitly bound the Faltings height of a curve over Q polynomially in its Belyi degree. Similar bounds are proven for three other Arakelov invariants: the discriminant, Faltings’ delta invariant and the self-intersection of the dualising sheaf. Our results allow us to explicitly bound these Arakelov invariants for modular curves, Hurwitz curves and Fermat curves in terms of their genus. Moreover, as an application, we show that the Couveignes‐Edixhoven‐Bruin algorithm to compute… Expand
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