In mathematics, complex dimension usually refers to the dimension of a complex manifold M, or complex algebraic variety V. If the complex dimension is d, the real dimension will be 2d. That is, the smooth manifold M has dimension 2d; and away from any singular points V will also be a smooth manifold of dimension 2d.
The same points apply to codimension. For example a smooth complex hypersurface in complex projective space of dimension n will be a manifold of dimension 2(n − 1). A complex hyperplane does not separate complex projective space into two components, because it has codimension 2.
Famous quotes containing the words complex and/or dimension:
“Specialization is a feature of every complex organization, be it social or natural, a school system, garden, book, or mammalian body.”
—Catharine R. Stimpson (b. 1936)
“By intervening in the Vietnamese struggle the United States was attempting to fit its global strategies into a world of hillocks and hamlets, to reduce its majestic concerns for the containment of communism and the security of the Free World to a dimension where governments rose and fell as a result of arguments between two colonels’ wives.”
—Frances Fitzgerald (b. 1940)