Let d ≥ 2 be an integer, let c ∈ Q̄(t) be a rational map, and let ft(z) := z+t z be a family of rational maps indexed by t. For each t = λ ∈ Q̄, we let ĥfλ (c(λ)) be the canonical height of c(λ) with respect to the rational map fλ; also we let ĥf (c) be the canonical height of c on the generic fiber of the above family of rational maps. We prove that there exists a constant C depending only on c ...

We study the gonality of a curve C and its canonical model $$C'$$ , by means unicuspidal rational curves, where those concepts can be better understood. start general formula for dimension space hypersurfaces fixed degree containing which we apply to some particular cases. Then classify curves via different notions gonality, model, up genus 6. do it using methods applied certain families arbitr...