Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Algebraic_curve> ?p ?o }
- Algebraic_curve abstract "In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.For example, the unit circle is an algebraic curve, being the set of zeros of the polynomial x2 + y2 − 1. Various technical considerations result in the complex zeros of a polynomial being considered as belonging to the curve. Also, the notion of algebraic curve has been generalized to allow the coefficients of the defining polynomial and the coordinates of the points of the curve to belong to any field, leading to the following definition.In algebraic geometry, a plane affine algebraic curve defined over a field k is the set of points of K2 whose coordinates are zeros of some bivariate polynomial with coefficients in k, where K is some algebraically closed extension of k. The points of the curve with coordinates in k are the k-points of the curve and, all together, are the k part of the curve.For example, (2,√−3) is a point of the curve defined by x2 + y2 − 1 = 0 and the usual unit circle is the real part of this curve. The term "unit circle" may refer to all the complex points as well to only the real points, the exact meaning usually clear from the context. The equation x2 + y2 + 1 = 0 defines an algebraic curve, whose real part is empty.More generally, one may consider algebraic curves that are not contained in the plane, but in a space of higher dimension. A curve that is not contained in some plane is called a skew curve. The simplest example of a skew algebraic curve is the twisted cubic. One may also consider algebraic curves contained in the projective space and even algebraic curves that are defined independently to any embedding in an affine or projective space. This leads to the most general definition of an algebraic curve:In algebraic geometry, an algebraic curve is an algebraic variety of dimension one.".
- Algebraic_curve thumbnail Tschirnhausen_cubic.svg?width=300.
- Algebraic_curve wikiPageID "253260".
- Algebraic_curve wikiPageLength "38890".
- Algebraic_curve wikiPageOutDegree "184".
- Algebraic_curve wikiPageRevisionID "679751744".
- Algebraic_curve wikiPageWikiLink Abelian_group.
- Algebraic_curve wikiPageWikiLink Acnode.
- Algebraic_curve wikiPageWikiLink Adequate_equivalence_relation.
- Algebraic_curve wikiPageWikiLink Affine_space.
- Algebraic_curve wikiPageWikiLink Algebraic_element.
- Algebraic_curve wikiPageWikiLink Algebraic_equation.
- Algebraic_curve wikiPageWikiLink Algebraic_function_field.
- Algebraic_curve wikiPageWikiLink Algebraic_geometry.
- Algebraic_curve wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Algebraic_curve wikiPageWikiLink Algebraic_set.
- Algebraic_curve wikiPageWikiLink Algebraic_variety.
- Algebraic_curve wikiPageWikiLink Algebraically_closed_field.
- Algebraic_curve wikiPageWikiLink American_Mathematical_Society.
- Algebraic_curve wikiPageWikiLink Arc_(geometry).
- Algebraic_curve wikiPageWikiLink Asymptote.
- Algebraic_curve wikiPageWikiLink Birational_geometry.
- Algebraic_curve wikiPageWikiLink Birkhäuser.
- Algebraic_curve wikiPageWikiLink Blowing_up.
- Algebraic_curve wikiPageWikiLink Bxc3xa9zouts_theorem.
- Algebraic_curve wikiPageWikiLink Cambridge_University_Press.
- Algebraic_curve wikiPageWikiLink Category:Algebraic_curves.
- Algebraic_curve wikiPageWikiLink Characteristic_(algebra).
- Algebraic_curve wikiPageWikiLink Claire_Voisin.
- Algebraic_curve wikiPageWikiLink Claude_Chevalley.
- Algebraic_curve wikiPageWikiLink Compact_space.
- Algebraic_curve wikiPageWikiLink Complex_number.
- Algebraic_curve wikiPageWikiLink Conic_section.
- Algebraic_curve wikiPageWikiLink Connected_space.
- Algebraic_curve wikiPageWikiLink Coordinate_system.
- Algebraic_curve wikiPageWikiLink Coordinates.
- Algebraic_curve wikiPageWikiLink Cramers_theorem_(algebraic_curves).
- Algebraic_curve wikiPageWikiLink Crunode.
- Algebraic_curve wikiPageWikiLink Cubic_plane_curve.
- Algebraic_curve wikiPageWikiLink Curve.
- Algebraic_curve wikiPageWikiLink Curve_sketching.
- Algebraic_curve wikiPageWikiLink Degree_of_a_continuous_mapping.
- Algebraic_curve wikiPageWikiLink Degree_of_a_polynomial.
- Algebraic_curve wikiPageWikiLink Differentiable_curve.
- Algebraic_curve wikiPageWikiLink Dimension_of_an_algebraic_variety.
- Algebraic_curve wikiPageWikiLink Elimination_theory.
- Algebraic_curve wikiPageWikiLink Elliptic_curve.
- Algebraic_curve wikiPageWikiLink Elliptic_function.
- Algebraic_curve wikiPageWikiLink Equivalence_of_categories.
- Algebraic_curve wikiPageWikiLink Ernst_Kötter.
- Algebraic_curve wikiPageWikiLink Euclidean_plane.
- Algebraic_curve wikiPageWikiLink Eulers_homogeneous_function_theorem.
- Algebraic_curve wikiPageWikiLink Faltings_theorem.
- Algebraic_curve wikiPageWikiLink Faltingss_theorem.
- Algebraic_curve wikiPageWikiLink Fermat_curve.
- Algebraic_curve wikiPageWikiLink Field_(mathematics).
- Algebraic_curve wikiPageWikiLink Field_extension.
- Algebraic_curve wikiPageWikiLink Fractional_ideal.
- Algebraic_curve wikiPageWikiLink Function_field_(scheme_theory).
- Algebraic_curve wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Algebraic_curve wikiPageWikiLink Fundamental_pair_of_periods.
- Algebraic_curve wikiPageWikiLink Fundamental_theorem_of_algebra.
- Algebraic_curve wikiPageWikiLink Genus_(mathematics).
- Algebraic_curve wikiPageWikiLink Genus_formula.
- Algebraic_curve wikiPageWikiLink Genus–degree_formula.
- Algebraic_curve wikiPageWikiLink Geometric_genus.
- Algebraic_curve wikiPageWikiLink George_Salmon.
- Algebraic_curve wikiPageWikiLink Glossary_of_algebraic_geometry.
- Algebraic_curve wikiPageWikiLink Glossary_of_scheme_theory.
- Algebraic_curve wikiPageWikiLink Gröbner_basis.
- Algebraic_curve wikiPageWikiLink Hilberts_sixteenth_problem.
- Algebraic_curve wikiPageWikiLink Holomorphic_function.
- Algebraic_curve wikiPageWikiLink Holomorphic_map.
- Algebraic_curve wikiPageWikiLink Homogeneous_coordinates.
- Algebraic_curve wikiPageWikiLink Homogeneous_function.
- Algebraic_curve wikiPageWikiLink Homogeneous_polynomial.
- Algebraic_curve wikiPageWikiLink Horst_Knörrer.
- Algebraic_curve wikiPageWikiLink Hyperbolic_geometry.
- Algebraic_curve wikiPageWikiLink Hyperelliptic_curve.
- Algebraic_curve wikiPageWikiLink Infinitely_near_point.
- Algebraic_curve wikiPageWikiLink Inflection_point.
- Algebraic_curve wikiPageWikiLink Intersection_number.
- Algebraic_curve wikiPageWikiLink Interval_(mathematics).
- Algebraic_curve wikiPageWikiLink Irreducible_component.
- Algebraic_curve wikiPageWikiLink Irreducible_polynomial.
- Algebraic_curve wikiPageWikiLink Jacobian_matrix_and_determinant.
- Algebraic_curve wikiPageWikiLink Jacobian_variety.
- Algebraic_curve wikiPageWikiLink Jean-Pierre_Serre.
- Algebraic_curve wikiPageWikiLink John_Milnor.
- Algebraic_curve wikiPageWikiLink John_Stillwell.
- Algebraic_curve wikiPageWikiLink Klein_quartic.
- Algebraic_curve wikiPageWikiLink Krull_dimension.
- Algebraic_curve wikiPageWikiLink Line_(geometry).
- Algebraic_curve wikiPageWikiLink List_of_curves.
- Algebraic_curve wikiPageWikiLink Manifold.
- Algebraic_curve wikiPageWikiLink Mathematics.
- Algebraic_curve wikiPageWikiLink Milnor-Jung_formula.
- Algebraic_curve wikiPageWikiLink Milnor_number.
- Algebraic_curve wikiPageWikiLink Monomial_order.
- Algebraic_curve wikiPageWikiLink Monotone_function.