Radical Parametrization of Algebraic Curves by Adjoint Curves

Abstract

We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less o equal to 4 and they are defined over an algebraically closed field of characteristic zero. In addition, we also present an algorithm for parametrizing by radicals any irreducible plane curve of degree $d$ having at least a point of multiplicity $d-r$, with $1\le r\le 4$ and, as a consequence, every irreducible plane curve of degree $d\le 5$ and every irreducible singular plane curve of degree 6.

16 pages. v3: title changed. v2: added part on conchoids, comments on the connection to Brill-Noether theory, other minor improvements

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