Linear Forms in Logarithms and Integer Points on Genus-two Curves

Abstract

We consider a linear form with algebraic coefficients, evaluated at points on the analytic Jacobian of a genus-two curve whose projective coordinates are algebraic. Previous results on the existence of a lower bound of a particular shape are made explicit. We study various properties of Jacobians of genus-two curves, paying particular attention to their embeddings into projective space, and give a method which can be used to find provably all integer points on a genus-two curve. We apply this method to one particular curve by way of example.