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. This amounts to determining the
genus of a curve: its complete singularity structure, computing
regular points of the curve in small coordinate fields, and
constructing linear systems of curves with prescribed intersection
multiplicities. The book discusses various optimality criteria for
rational parametrizations of algebraic curves.
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