Algebraic curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0. These two operations are each inverse to the other; therefore, the phrase algebraic plane curve is often used without specifying explicitly whether it is the affine or the projective case that is considered.
known for
Wikipage disambiguates
AF+BG theoremAbel's theoremAbelian extensionAbelian integralAbelian varietyAbel–Jacobi mapAbhyankar's conjectureAdele ringAdolf HurwitzAffine GrassmannianAffine algebraic curveAffine varietyAleksei ParshinAlexander GrothendieckAlfred KempeAlgebraic CurvesAlgebraic curvesAlgebraic cycleAlgebraic functionAlgebraic geometryAlgebraic geometry and analytic geometryAlgebraic number fieldAlgebraic number theoryAlgebraic plane curveAlgebraic statisticsAlgebraic surfaceAlgebraic varietyAlgebraical curveAmple line bundleAnabelian geometryAnalytic subgroup theoremArc lengthAreas of mathematicsArithmetic surfaceArithmetic zeta functionAstroidAsymptoteAtriphtaloidBass conjectureBeauville–Laszlo theorem
Link from a Wikipage to another Wikipage
known for
sub discipline
seeAlso
primaryTopic
Algebraic curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0. These two operations are each inverse to the other; therefore, the phrase algebraic plane curve is often used without specifying explicitly whether it is the affine or the projective case that is considered.
has abstract
Em geometria algébrica, uma cu ...... culos e outras seções cônicas.
@pt
En geometria algebraica, una c ...... umferències i altres còniques.
@ca
En geometría algebraica, una c ...... cia y otras secciones cónicas.
@es
En mathématiques, et plus préc ...... ns d'une équation polynomiale.
@fr
In de algebraïsche meetkunde i ...... ameling van deze vergelijking.
@nl
In mathematics, an affine alge ...... a space curve or a skew curve.
@en
Алгебраическая кривая или плос ...... торого состоят из одной точки.
@ru
Алгебричні криві — це найпрост ...... го складаються з однієї точки.
@uk
في الهندسة الجبرية، المنحني ال ...... ها بالمعادلة س2 + ص2 - 1 = 0 .
@ar
在代數幾何中,一條代數曲線是一維的代數簇。最典型的例子是射影平面上由一個齊次多項式定義的零點。
@zh
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,016,857,602
Link from a Wikipage to another Wikipage
wikiPageUsesTemplate
subject
hypernym
type
comment
Em geometria algébrica, uma cu ...... culos e outras seções cônicas.
@pt
En geometria algebraica, una c ...... umferències i altres còniques.
@ca
En geometría algebraica, una c ...... cia y otras secciones cónicas.
@es
En mathématiques, et plus préc ...... ns d'une équation polynomiale.
@fr
In de algebraïsche meetkunde i ...... coëfficiënten zijn element van
@nl
In mathematics, an affine alge ...... ctive case that is considered.
@en
Алгебраическая кривая или плос ...... ся уравнением x2 + y2 − 1 = 0.
@ru
Алгебричні криві — це найпрост ...... ня на випадок довільного поля.
@uk
في الهندسة الجبرية، المنحني ال ...... ها بالمعادلة س2 + ص2 - 1 = 0 .
@ar
在代數幾何中,一條代數曲線是一維的代數簇。最典型的例子是射影平面上由一個齊次多項式定義的零點。
@zh
label
Algebra kurbo
@eo
Algebraic curve
@en
Algebraische Kurve
@de
Algebraïsche kromme
@nl
Corba algebraica
@ca
Courbe algébrique
@fr
Curva algebraica
@es
Curva algébrica
@pt
Алгебраическая кривая
@ru
Алгебрична крива
@uk