TAMING GENUS 0 (OR 1) COMPONENTS ON VARIABLES-SEPARATED EQUATIONS
TAMING GENUS 0 (OR 1) COMPONENTS ON VARIABLES-SEPARATED EQUATIONS
To describe curves of form Cf,g=def(x,y)|f(x)−g(y)=0 and their number theory properties, you must address Cf,g whose projective normalization has a genus 0 (or 1) component. For f and g polynomials and f indecomposable, [Fr73a] distinguished Cf,g with u=1 versus u>1 components (Schinzel’s problem). For u=1, [Fr73b, (1.6) of Prop. 1] …