structural:reformatting
Algebraic manifolds

An algebraic manifold is an algebraic variety that is also an m -dimensional manifold, and hence every sufficiently small local patch is isomorphic to k. Equivalently, the variety is smooth (free from singular points). When k is the real numbers, R, algebraic manifolds are called Nash manifolds. Algebraic manifolds can be defined as the zero set of a finite collection of analytic algebraic functions. Projective algebraic manifolds are an equivalent definition for projective varieties. The Riemann sphere is one example.