Radical parametrizations of algebraic curves by adjoint curves
Copyright policy )Radical parametrizations of algebraic curves by adjoint curves
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.
16 pages. v3: title changed. v2: added part on conchoids, comments on the connection to Brill-Noether theory, other minor improvements
Computational aspects of algebraic curves, Algebra and Number Theory, Parametrization by adjoint curves, radical parametrization, Conchoids, Offset curves, offset curves, conchoids, 14Q05, 12Y05, parametrization by adjoint curves, Computational Mathematics, Mathematics - Algebraic Geometry, FOS: Mathematics, Algebraic functions and function fields in algebraic geometry, Radical parametrization, Algebraic Geometry (math.AG)
Computational aspects of algebraic curves, Algebra and Number Theory, Parametrization by adjoint curves, radical parametrization, Conchoids, Offset curves, offset curves, conchoids, 14Q05, 12Y05, parametrization by adjoint curves, Computational Mathematics, Mathematics - Algebraic Geometry, FOS: Mathematics, Algebraic functions and function fields in algebraic geometry, Radical parametrization, Algebraic Geometry (math.AG)
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