Complex dimension

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.

This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.v · Categories: Complex manifolds Algebraic geometry Dimension Mathematical analysis stubs Wikimedia Foundation. 2010. Игры ⚽ Нужно сделать НИР? Model Arts and Niland Gallery Sestri Levante Look at other dictionaries: Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …   Wikipedia Complex analysis — Plot of the function f(x)=(x2 1)(x 2 i)2/(x2 + 2 + 2i). The hue represents the function argument, while the brightness represents the magnitude. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch …   Wikipedia Complex polygon — The term complex polygon can mean two different things: In computer graphics, as a polygon which is neither convex nor concave. In geometry, as a polygon in the unitary plane, which has two complex dimensions. Contents 1 Computer graphics 2… …   Wikipedia Dimension (disambiguation) — A dimension is a spatial characteristic of an object; that is, length, width, or height. Dimension may also be: Contents 1 Science: 2 Mathematics: 3 Media: 4 Other …   Wikipedia Complex torus — In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the… …   Wikipedia Complex hearts — is a variant of Hearts reported to be invented by Richard Garfield. It uses the complex number system for scoring. The rules of play are similar to those of conventional Hearts.coring*Hearts are worth 1 + 0i points apiece. * J♦ is worth 10 + 0i… …   Wikipedia Complex network zeta function — Different definitions have been given for the dimension of a complex network or graph. For example, metric dimension is defined in terms of the resolving set for a graph. Dimension has also been defined based on the box covering method applied to …   Wikipedia Dimension — 0d redirects here. For 0D, see 0d (disambiguation). For other uses, see Dimension (disambiguation). From left to right, the square, the cube, and the tesseract. The square is bounded by 1 dimensional lines, the cube by 2 dimensional areas, and… …   Wikipedia Dimension (vector space) — In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. This description… …   Wikipedia Complex space — In mathematics, n dimensional complex space is a multi dimensional generalisation of the complex numbers, which have both real and imaginary parts or dimensions. The n dimensional complex space can be seen as n cartesian products of the complex… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”