Projective algebraic manifold

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In mathematics, a projective algebraic manifold is a complex manifold which is a submanifold of a complex projective space which is determined by the zeros of a set of homogeneous polynomials.

For example if for r in R and pr is the polynomial C2 → C : (x, y) → x2 + y2 - r2, then

N := \{ \mathbf{C}(x, y) | (x, y) \in \mathbf{C}, p_r(x, y) = 0 \}

is a projective algebraic manifold.

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