an algebraic set of dimension one is also called an algebraic curve, but this will not be the case in this article.) Equivalently, an algebraic curve is...

space and skew curves apply also to real algebraic curves, although the above definition of a curve does not apply (a real algebraic curve may be disconnected)...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

(genus 3) Bring's curve (genus 4) Macbeath surface (genus 7) Butterfly curve (algebraic) (genus 7) Polynomial lemniscate Fermat curve Sinusoidal spiral...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over...

smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose...

of genus of any projective algebraic scheme X: the arithmetic genus and the geometric genus. When X is an algebraic curve with field of definition the...

in algebraic geometry. The analogue of a Riemann surface is a non-singular algebraic curve C over a field k. The difference in terminology (curve vs....

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism...

precise definition of a singular point depends on the type of curve being studied. Algebraic curves in the plane may be defined as the set of points (x, y)...

In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: A x 4...

gonality of an algebraic curve C is defined as the lowest degree of a nonconstant rational map from C to the projective line. In more algebraic terms, if C...

mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with...

containing no such points). This is an example of an algebraic curve. Every elliptic curve is an algebraic curve, given by (the compactification of) the locus...

singularities were first noticed in the study of algebraic curves. The double point at (0, 0) of the curve y 2 = x 2 + x 3 {\displaystyle y^{2}=x^{2}+x^{3}}...

In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of...

the curve, curvilinear asymptotes have also been used although the term asymptotic curve seems to be preferred. The asymptotes of an algebraic curve in...

In algebraic geometry, a lemniscate (/lɛmˈnɪskɪt/ or /ˈlɛmnɪsˌkeɪt, -kɪt/) is any of several figure-eight or ∞-shaped curves. The word comes from the...

In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric...

space which one can restrict to the algebraic variety. By definition, if ω is the Kähler metric on the algebraic variety X and the canonical bundle KX...

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...

example of an algebraic curve. From the point of view of algebraic geometry, P1(K) is a non-singular curve of genus 0. If K is algebraically closed, it is...

In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients...

references to algebraic geometry codes throughout 1980s and 1990s coding theory literature. In this section the construction of algebraic geometry codes...

(mathematics)#Behavior of a polynomial function near a multiple root Algebraic curve#Tangent at a point In "Nova Methodus pro Maximis et Minimis" (Acta...

of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and...

{\displaystyle k(Y)} ). We see that the degree of an algebraic function field is not a well-defined notion. The algebraic function fields over k form a category; the...

In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y 2 + h ( x ) y = f ( x ) {\displaystyle...

) {\displaystyle (0,0)} . For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry...