Radical Parametrization of Algebraic Curves by Adjoint Curves

Details Radical Parametrization of Algebraic Curves by Adjoint Curves Radical Parametrization of Algebraic Curves by Adjoint Curves

2008-05-21

arxiv.org/abs/0805.3214v3

Journal of Symbolic Computation Volume 46, Issue 9, September 2011, Pages 1030-1038

Mathematics

Algebraic Geometry

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

Scientific paper

10.1016/j.jsc.2011.05.005

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 $1\leq r \leq 4$ and, as a consequence, every irreducible plane curve of degree $d \leq 5$ and every irreducible singular plane curve of degree 6.

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