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- Algebraic_manifold abstract "In mathematics, 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 defined by polynomials. An example is the sphere, which can be defined as the zero set of the polynomial x2 + y2 + z2 – 1, and hence is an algebraic variety. For an algebraic manifold, the ground field will be the real numbers or complex numbers; in the case of the real numbers, the manifold of real points is sometimes called a Nash manifold.Every sufficiently small local patch of an algebraic manifold is isomorphic to km where k is the ground field. Equivalently the variety is smooth (free from singular points). The Riemann sphere is one example of a complex algebraic manifold, since it is the complex projective line.".
- Algebraic_manifold wikiPageExternalLink AlgebraicManifold.html.
- Algebraic_manifold wikiPageExternalLink KAlgebraicManifold.html.
- Algebraic_manifold wikiPageExternalLink lec-23.ps.gz.
- Algebraic_manifold wikiPageID "4499397".
- Algebraic_manifold wikiPageLength "1841".
- Algebraic_manifold wikiPageOutDegree "23".
- Algebraic_manifold wikiPageRevisionID "663975986".
- Algebraic_manifold wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Algebraic_manifold wikiPageWikiLink Algebraic_variety.
- Algebraic_manifold wikiPageWikiLink Annals_of_Mathematics.
- Algebraic_manifold wikiPageWikiLink Category:Algebraic_varieties.
- Algebraic_manifold wikiPageWikiLink Category:Manifolds.
- Algebraic_manifold wikiPageWikiLink Complex_number.
- Algebraic_manifold wikiPageWikiLink Complex_numbers.
- Algebraic_manifold wikiPageWikiLink Complex_projective_line.
- Algebraic_manifold wikiPageWikiLink Curve.
- Algebraic_manifold wikiPageWikiLink Differentiable_manifold.
- Algebraic_manifold wikiPageWikiLink Elliptic_curve.
- Algebraic_manifold wikiPageWikiLink Grassmannian.
- Algebraic_manifold wikiPageWikiLink Ground_field.
- Algebraic_manifold wikiPageWikiLink Manifold.
- Algebraic_manifold wikiPageWikiLink Mathematics.
- Algebraic_manifold wikiPageWikiLink Nash_functions.
- Algebraic_manifold wikiPageWikiLink Nash_manifold.
- Algebraic_manifold wikiPageWikiLink Polynomial.
- Algebraic_manifold wikiPageWikiLink Real_number.
- Algebraic_manifold wikiPageWikiLink Riemann_sphere.
- Algebraic_manifold wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Algebraic_manifold wikiPageWikiLink Smooth_function.
- Algebraic_manifold wikiPageWikiLink Smooth_manifold.
- Algebraic_manifold wikiPageWikiLink Smoothness.
- Algebraic_manifold wikiPageWikiLink Sphere.
- Algebraic_manifold wikiPageWikiLink Surface.
- Algebraic_manifold wikiPageWikiLink Surfaces.
- Algebraic_manifold wikiPageWikiLink Zero_set.
- Algebraic_manifold wikiPageWikiLinkText "Algebraic manifold".
- Algebraic_manifold wikiPageWikiLinkText "algebraic manifold".
- Algebraic_manifold wikiPageWikiLinkText "algebraic".
- Algebraic_manifold hasPhotoCollection Algebraic_manifold.
- Algebraic_manifold wikiPageUsesTemplate Template:Cite_journal.
- Algebraic_manifold subject Category:Algebraic_varieties.
- Algebraic_manifold subject Category:Manifolds.
- Algebraic_manifold hypernym Variety.
- Algebraic_manifold type Article.
- Algebraic_manifold type Grape.
- Algebraic_manifold type Article.
- Algebraic_manifold type Space.
- Algebraic_manifold type Variety.
- Algebraic_manifold comment "In mathematics, 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 defined by polynomials. An example is the sphere, which can be defined as the zero set of the polynomial x2 + y2 + z2 – 1, and hence is an algebraic variety.".
- Algebraic_manifold label "Algebraic manifold".
- Algebraic_manifold sameAs m.0c5pmb.
- Algebraic_manifold sameAs Q4724008.
- Algebraic_manifold sameAs Q4724008.
- Algebraic_manifold wasDerivedFrom Algebraic_manifold?oldid=663975986.
- Algebraic_manifold isPrimaryTopicOf Algebraic_manifold.