An algebraic curve is a one-dimensional algebraic variety. An affine plane algebraic curve over a field is the locus defined by an equation , where is a nonconstant polynomial with coefficients in . A nonsingular algebraic curve has no singular points over an algebraic closure of . A point on the plane curve is a solution of its equation, with coordinates in or an extension field. A -rational point has both coordinates in .

The following table lists the names of algebraic curves of a given degree.

See also

Algebraic Geometry, Algebraic Variety, Character Variety, Curve, Etale Morphism, p-adic Section Conjecture

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References

Arbarello, E.; Cornalba, M.; Griffiths, P. A.; and Harris, J. Geometry of Algebraic Curves, I. New York: Springer-Verlag, 1985.Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, 1959.Griffiths, P. A. Introduction to Algebraic Curves. Providence, RI: Amer. Math. Soc., 1989.Krishnan, S. and Manocha, D. "Numeric-Symbolic Algorithms for Evaluating One-Dimensional Algebraic Sets." In Proc. 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC '95 (Ed. A. H. M. Levelt). New York: ACM Press, pp. 59-67, 1995. https://doi.org/10.1145/220346.220354.

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Algebraic Curve

Cite this as:

Weisstein, Eric W. "Algebraic Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicCurve.html

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