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- 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 in one variable with complex coefficients (an algebraic object) is determined by the set of its roots (a geometric object). 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 specifity 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 wikiPageRevisionID "604807297".
- Algebraic_variety hasPhotoCollection Algebraic_variety.
- Algebraic_variety id "6838".
- Algebraic_variety title "Isomorphism of varieties".
- Algebraic_variety subject Category:Algebraic_geometry.
- Algebraic_variety subject Category:Algebraic_varieties.
- Algebraic_variety type Abstraction100002137.
- Algebraic_variety type AlgebraicVarieties.
- Algebraic_variety type Assortment108398773.
- Algebraic_variety type Collection107951464.
- Algebraic_variety type Group100031264.
- Algebraic_variety comment "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.".
- Algebraic_variety label "Algebraic variety".
- Algebraic_variety label "Algebraische Varietät".
- Algebraic_variety label "Algebraïsche variëteit".
- Algebraic_variety label "Rozmaitość algebraiczna".
- Algebraic_variety label "Variedad algebraica".
- Algebraic_variety label "Variedade algébrica".
- Algebraic_variety label "Varietà algebrica".
- Algebraic_variety label "Variété algébrique".
- Algebraic_variety label "Алгебраическое многообразие".
- Algebraic_variety label "تنوع جبري".
- Algebraic_variety label "代数多様体".
- Algebraic_variety label "代数簇".
- Algebraic_variety sameAs Algebraická_varieta.
- Algebraic_variety sameAs Algebraische_Varietät.
- Algebraic_variety sameAs Variedad_algebraica.
- Algebraic_variety sameAs Variété_algébrique.
- Algebraic_variety sameAs Varietas_aljabar.
- Algebraic_variety sameAs Varietà_algebrica.
- Algebraic_variety sameAs 代数多様体.
- Algebraic_variety sameAs 대수다양체.
- Algebraic_variety sameAs Algebraïsche_variëteit.
- Algebraic_variety sameAs Rozmaitość_algebraiczna.
- Algebraic_variety sameAs Variedade_algébrica.
- Algebraic_variety sameAs m.01kzm4.
- Algebraic_variety sameAs Q648995.
- Algebraic_variety sameAs Q648995.
- Algebraic_variety sameAs Algebraic_variety.
- Algebraic_variety wasDerivedFrom Algebraic_variety?oldid=604807297.
- Algebraic_variety depiction Twisted_cubic_curve.png.
- Algebraic_variety isPrimaryTopicOf Algebraic_variety.
