Projective algebraic manifold

Projective algebraic manifold

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 "p""r" 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.

ee also

*Chow's theorem


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Algebraic manifold — An algebraic manifold is an algebraic variety which is also a manifold. As such, algebraic manifolds are a generalisation of the concept of smooth curves and surfaces. An example is the sphere, which can be defined as the zero set of the… …   Wikipedia

  • Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… …   Wikipedia

  • Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

  • Algebraic variety — This article is about algebraic varieties. For the term a variety of algebras , and an explanation of the difference between a variety of algebras and an algebraic variety, see variety (universal algebra). The twisted cubic is a projective… …   Wikipedia

  • Algebraic geometry and analytic geometry — In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally… …   Wikipedia

  • Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

  • Projective plane — See real projective plane and complex projective plane, for the cases met as manifolds of respective dimension 2 and 4 In mathematics, a projective plane has two possible definitions, one of them coming from linear algebra, and another (which is… …   Wikipedia

  • Projective line — In mathematics, a projective line is a one dimensional projective space. The projective line over a field K , denoted P1( K ), may be defined as the set of one dimensional subspaces of the two dimensional vector space K 2 (it does carry other… …   Wikipedia

  • Algebraic surface — In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface is therefore of complex dimension two (as a complex manifold, when it is non singular)… …   Wikipedia

  • Projective module — In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”