High Quality Content by WIKIPEDIA articles! In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections. An algebraic curve defined over a field F may be considered as the locus of points in Fn determined by at least n ? 1 independent polynomial functions in n variables with coefficients in F, gi(x1, …, xn), where the curve is defined by setting each gi = 0. Using the resultant, we can eliminate all but two of the variables and reduce the curve to a birationally equivalent plane curve, f(x, y) = 0, still with coefficients in F, but usually of higher degree, and often possessing additional singularities.

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