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  2. Algebraic curve - Wikipedia

    en.wikipedia.org/wiki/Algebraic_curve

    An algebraic curve in the Euclidean plane is the set of the points whose coordinates are the solutions of a bivariate polynomial equation p(x, y) = 0.This equation is often called the implicit equation of the curve, in contrast to the curves that are the graph of a function defining explicitly y as a function of x.

  3. Gallery of curves - Wikipedia

    en.wikipedia.org/wiki/Gallery_of_curves

    1 Algebraic curves. ... Download as PDF; Printable version; ... This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves. ...

  4. Curve - Wikipedia

    en.wikipedia.org/wiki/Curve

    A space curve is a curve for which is at least three-dimensional; a skew curve is a space curve which lies in no plane. These definitions of plane, 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 ).

  5. List of curves - Wikipedia

    en.wikipedia.org/wiki/List_of_curves

    1.1 Algebraic curves. 1.1.1 Rational curves. ... Download as PDF; ... This is a list of Wikipedia articles about curves used in different fields: mathematics ...

  6. Algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry

    Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.

  7. Geometry - Wikipedia

    en.wikipedia.org/wiki/Geometry

    In topology, a curve is defined by a function from an interval of the real numbers to another space. [49] In differential geometry, the same definition is used, but the defining function is required to be differentiable. [53] Algebraic geometry studies algebraic curves, which are defined as algebraic varieties of dimension one. [54]

  8. Scheme (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Scheme_(mathematics)

    In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).

  9. Anabelian geometry - Wikipedia

    en.wikipedia.org/wiki/Anabelian_geometry

    A concrete example is the case of curves, which may be affine as well as projective. Suppose given a hyperbolic curve C, i.e., the complement of n points in a projective algebraic curve of genus g, taken to be smooth and irreducible, defined over a field K that is finitely generated (over its prime field), such that <.

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