In mathematics, an algebraic surface is an algebraic variety of dimension two. Thus, an algebraic surface is a solution of a set of polynomial equations, in which there are two independent directions at every point. An example of an algebraic surface is the sphere, which is determined by the single polynomial equation x2+y2+z2=1.{\displaystyle x^{2}+y^{2}+z^{2}=1.} Studying the intrinsic geometry of algebraic surfaces is a central topic in algebraic geometry.
