Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Algebraic_variety> ?p ?o }
- Algebraic_variety abstract "In mathematics, algebraic varieties (also called varieties) are one of the central objects of study in algebraic geometry. Classically, an algebraic variety was defined to be the set of solutions of a system of polynomial equations, over the real or complex numbers. Modern definitions of an algebraic variety generalize this notion in several different ways, while attempting to preserve the geometric intuition behind the original definition.Conventions regarding the definition of an algebraic variety differ slightly. For example, some authors require that an "algebraic variety" is, by definition, irreducible (which means that it is not the union of two smaller sets that are closed in the Zariski topology), while others do not. When the former convention is used, non-irreducible algebraic varieties are called algebraic sets.The notion of variety is similar to that of manifold, the difference being that a variety may have singular points, while a manifold will not. In many languages, both varieties and manifolds are named by the same word.Proven around the year 1800, the fundamental theorem of algebra establishes a link between algebra and geometry by showing that a monic polynomial (an algebraic object) in one variable with complex coefficients is determined by the set of its roots (a geometric object) in the complex plane. Generalizing this result, Hilbert's Nullstellensatz provides a fundamental correspondence between ideals of polynomial rings and algebraic sets. Using the Nullstellensatz and related results, mathematicians have established a strong correspondence between questions on algebraic sets and questions of ring theory. This correspondence is the specificity of algebraic geometry among the other subareas of geometry.".
- Algebraic_variety thumbnail Twisted_cubic_curve.png?width=300.
- Algebraic_variety wikiPageExternalLink ag.html.
- Algebraic_variety wikiPageID "248808".
- Algebraic_variety wikiPageLength "26479".
- Algebraic_variety wikiPageOutDegree "151".
- Algebraic_variety wikiPageRevisionID "682225800".
- Algebraic_variety wikiPageWikiLink Abelian_variety.
- Algebraic_variety wikiPageWikiLink Absolutely_irreducible.
- Algebraic_variety wikiPageWikiLink Abstract_algebraic_variety.
- Algebraic_variety wikiPageWikiLink Affine_space.
- Algebraic_variety wikiPageWikiLink Alexander_Grothendieck.
- Algebraic_variety wikiPageWikiLink Algebra.
- Algebraic_variety wikiPageWikiLink Algebraic_curve.
- Algebraic_variety wikiPageWikiLink Algebraic_geometry.
- Algebraic_variety wikiPageWikiLink Algebraic_geometry_of_projective_spaces.
- Algebraic_variety wikiPageWikiLink Algebraic_manifold.
- Algebraic_variety wikiPageWikiLink Algebraic_space.
- Algebraic_variety wikiPageWikiLink Algebraic_stack.
- Algebraic_variety wikiPageWikiLink Algebraic_surface.
- Algebraic_variety wikiPageWikiLink Algebraic_variety.
- Algebraic_variety wikiPageWikiLink Algebraically_closed_field.
- Algebraic_variety wikiPageWikiLink Analytic_variety.
- Algebraic_variety wikiPageWikiLink André_Weil.
- Algebraic_variety wikiPageWikiLink Birational_geometry.
- Algebraic_variety wikiPageWikiLink Category:Algebraic_geometry.
- Algebraic_variety wikiPageWikiLink Category:Algebraic_varieties.
- Algebraic_variety wikiPageWikiLink Category_theory.
- Algebraic_variety wikiPageWikiLink Characteristic_class.
- Algebraic_variety wikiPageWikiLink Chern_class.
- Algebraic_variety wikiPageWikiLink Claude_Chevalley.
- Algebraic_variety wikiPageWikiLink Closed_immersion.
- Algebraic_variety wikiPageWikiLink Closed_set.
- Algebraic_variety wikiPageWikiLink Coherent_sheaf.
- Algebraic_variety wikiPageWikiLink Complete_variety.
- Algebraic_variety wikiPageWikiLink Complex-analytic_variety.
- Algebraic_variety wikiPageWikiLink Complex_number.
- Algebraic_variety wikiPageWikiLink Complex_numbers.
- Algebraic_variety wikiPageWikiLink Complex_plane.
- Algebraic_variety wikiPageWikiLink Constructible_set_(topology).
- Algebraic_variety wikiPageWikiLink Dimension_of_an_algebraic_variety.
- Algebraic_variety wikiPageWikiLink Elliptic_curve.
- Algebraic_variety wikiPageWikiLink Exterior_algebra.
- Algebraic_variety wikiPageWikiLink Exterior_power.
- Algebraic_variety wikiPageWikiLink Factorization_of_polynomials.
- Algebraic_variety wikiPageWikiLink Fiber_product.
- Algebraic_variety wikiPageWikiLink Foundations_of_Algebraic_Geometry.
- Algebraic_variety wikiPageWikiLink Function_(mathematics).
- Algebraic_variety wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Algebraic_variety wikiPageWikiLink Fundamental_theorem_of_algebra.
- Algebraic_variety wikiPageWikiLink Genus_formula.
- Algebraic_variety wikiPageWikiLink Genus–degree_formula.
- Algebraic_variety wikiPageWikiLink Geometry.
- Algebraic_variety wikiPageWikiLink Glossary_of_algebraic_geometry.
- Algebraic_variety wikiPageWikiLink Glossary_of_scheme_theory.
- Algebraic_variety wikiPageWikiLink Graph_isomorphism.
- Algebraic_variety wikiPageWikiLink Grassmannian.
- Algebraic_variety wikiPageWikiLink Grassmannian_variety.
- Algebraic_variety wikiPageWikiLink Gröbner_basis.
- Algebraic_variety wikiPageWikiLink Hilberts_Nullstellensatz.
- Algebraic_variety wikiPageWikiLink Homogeneous_coordinate_ring.
- Algebraic_variety wikiPageWikiLink Homogeneous_coordinates.
- Algebraic_variety wikiPageWikiLink Homogeneous_polynomial.
- Algebraic_variety wikiPageWikiLink Homogeneous_polynomials.
- Algebraic_variety wikiPageWikiLink Hypersurface.
- Algebraic_variety wikiPageWikiLink Ideal_(ring_theory).
- Algebraic_variety wikiPageWikiLink Identity_function.
- Algebraic_variety wikiPageWikiLink If_and_only_if.
- Algebraic_variety wikiPageWikiLink Injective_function.
- Algebraic_variety wikiPageWikiLink Integral_domain.
- Algebraic_variety wikiPageWikiLink Jean-Pierre_Serre.
- Algebraic_variety wikiPageWikiLink Line_(geometry).
- Algebraic_variety wikiPageWikiLink Locally_free_sheaf.
- Algebraic_variety wikiPageWikiLink Locally_ringed_space.
- Algebraic_variety wikiPageWikiLink Manifold.
- Algebraic_variety wikiPageWikiLink Masayoshi_Nagata.
- Algebraic_variety wikiPageWikiLink Mathematics.
- Algebraic_variety wikiPageWikiLink Moduli_of_algebraic_curves.
- Algebraic_variety wikiPageWikiLink Monic_polynomial.
- Algebraic_variety wikiPageWikiLink Monomial_order.
- Algebraic_variety wikiPageWikiLink Morphism_of_algebraic_varieties.
- Algebraic_variety wikiPageWikiLink Morphism_of_varieties.
- Algebraic_variety wikiPageWikiLink Motive_(algebraic_geometry).
- Algebraic_variety wikiPageWikiLink Nash_functions.
- Algebraic_variety wikiPageWikiLink Nash_manifold.
- Algebraic_variety wikiPageWikiLink Natural_topology.
- Algebraic_variety wikiPageWikiLink Nilpotent.
- Algebraic_variety wikiPageWikiLink Nilradical_of_a_ring.
- Algebraic_variety wikiPageWikiLink Plücker_embedding.
- Algebraic_variety wikiPageWikiLink Polynomial_algebra.
- Algebraic_variety wikiPageWikiLink Polynomial_factorization.
- Algebraic_variety wikiPageWikiLink Polynomial_ring.
- Algebraic_variety wikiPageWikiLink Prime_ideal.
- Algebraic_variety wikiPageWikiLink Projective_algebraic_manifold.
- Algebraic_variety wikiPageWikiLink Projective_line.
- Algebraic_variety wikiPageWikiLink Projective_space.
- Algebraic_variety wikiPageWikiLink Projective_variety.
- Algebraic_variety wikiPageWikiLink Pullback_(category_theory).
- Algebraic_variety wikiPageWikiLink Quasi-projective_variety.
- Algebraic_variety wikiPageWikiLink Quasiprojective_variety.