An algebraic curve over a Field is an equation , where is a Polynomial in and with Coefficients in . A nonsingular algebraic curve is an algebraic curve over which has no Singular Points over . A point on an algebraic curve is simply a solution of the equation of the curve. A -Rational Point is a point on the curve, where and are in the Field .
See also Algebraic Geometry, Algebraic Variety, Curve
Griffiths, P. A. Introduction to Algebraic Curves. Providence, RI: Amer. Math. Soc., 1989.