The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization.

The central problem considered in this book is the determination of rational parametrizability of an algebraic curve, and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve, i.e. its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. Various optimality criteria for rational parametrizations of algebraic curves are discussed. This book is mainly intended for graduate students and researchers in constructive algebraic curve geometry. It provides a nice and easy introduction to the topic for students.

Nice and easy introduction to topic for students Includes supplementary material: sn.pub/extras

Contenu
and Motivation.- Plane Algebraic Curves.- The Genus of a Curve.- Rational Parametrization.- Algebraically Optimal Parametrization.- Rational Reparametrization.- Real Curves.