Concept information
Terme préférentiel
algebraic curve
Définition
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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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Algebraic_curve)
Concept générique
Concepts spécifiques
- abelian integral
- abelian variety
- Abel-Jacobi map
- acnode
- Belyi's theorem
- Bézout's theorem
- bitangent
- Brill-Noether theory
- Bring's curve
- cardioid
- cissoid
- Cramer's paradox
- cubic plane curve
- dessin d'enfant
- dual curve
- elliptic curve
- Fermat curve
- folium of Descartes
- Hasse-Witt matrix
- hyperelliptic curve
- Klein quartic
- lemniscate of Gerono
- modular curve
- modularity theorem
- Plücker formula
- polar curve
- projective line
- quartic plane curve
- real plane curve
- Riemann-Hurwitz formula
- singular point of a curve
- sinusoidal spiral
- smooth completion
- squircle
- stable curve
- superegg
- theta characteristic
- theta divisor
- Torelli theorem
- Weber's theorem
- Weierstrass elliptic function
- Weierstrass point
- Weil reciprocity law
Traductions
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français
URI
http://data.loterre.fr/ark:/67375/PSR-QP0D47D3-D
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