Rational Points on Algebraic Curves That Change Genus Original Research Article

LetKbe an algebraic function field in one variable over an algebraically closed field of positive characteristicp. We give an explicit upper bound for the number of rational points of genus-changing curves overKdefined byyp=r(x) and show that every genus-changing curve of absolute genus 0 has finitely manyK-rational points. We thus prove that every algebraic curve overKthat admits genus change under base-field extensions has finitely manyK-rational points.