Integer points and models of algebraic curves
This paper describes a method for the construction of models of algebraic curves \(F(X, Y)=0\) of genus \(\geq 1\) defined over a number field, and the effective computation of integer points on such models. This construction is applied to the problem of the effective determination of integer points on curves of genus 2 by reducing this problem to that of effectively computing integer points on quartic equations defined over a number field. The results obtained are also applied to give explicit upper bounds for the heights of integer points on a family of curves \(F(X, Y)=0\) defined over a number field, which are cyclic coverings of the projective line.
explicit upper bounds for the heights of integer points
scientific article; zbMATH DE number 650853
scientific article