Algebraic geometry/Related Articles

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A list of Citizendium articles, and planned articles, about Algebraic geometry.
See also changes related to Algebraic geometry, or pages that link to Algebraic geometry or to this page or whose text contains "Algebraic geometry".

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  • Abelian surface [r]: A 2-dimensional Abelian variety. [e]
  • Abelian variety [r]: A complete non-singular projective variety which is also an algebraic group, necessarily abelian; a complex torus. [e]
  • Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields. [e]
  • Adjunction formula [r]: Formula of algebraic geometry and complex manifold theory relates, for a hypersurface, its normal bundle, its canonical bundle, and the canonical bundle of the ambient variety or manifold. [e]
  • Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]
  • Basis (mathematics) [r]: Add brief definition or description
  • Canonical sheaf [r]: In algebraic geometry, differential geometry, and differential topology, the top wedge product of the cotangent sheaf. [e]
  • Commutative algebra [r]: Branch of mathematics studying commutative rings and related structures. [e]
  • Ernst Eduard Kummer [r]: (29 January 1810 - 14 May 1893) German mathematician who codified some of the relations between different hypergeometric series, proved Fermat's last theorem for a considerable class of prime exponents, and found the Kummer surface. [e]
  • Generic point [r]: A point of a topological space which is not contained in any proper closed subset; a point satisfying no special properties. [e]
  • Genus-degree formula [r]: Formula which relates the degree d of a non-singular plane curve with its arithmetic genus g. [e]
  • Hyperelliptic curve [r]: An algebraic curve given by an equation of the form y2 = f(x). [e]
  • Isogeny [r]: Morphism of varieties between two abelian varieties (e.g. elliptic curves) that is surjective and has a finite kernel. [e]
  • K3 surface [r]: Complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle. [e]
  • Kummer surface [r]: An irreducible algebraic surface of degree 4 in P3 with the maximal possible number of 16 double points. [e]
  • Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
  • Polynomial equation [r]: An equation in which a polynomial in one or more variables is set equal to zero. [e]
  • Riemann-Hurwitz formula [r]: Formula which describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. [e]
  • Riemann-Roch theorem [r]: Theorem that relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings. [e]
  • Scheme (mathematics) [r]: Topological space together with commutative rings for all its open sets, which arises from 'glueing together' spectra (spaces of prime ideals) of commutative rings. [e]
  • Étale morphism [r]: An algebraic analogue of the notion of a local isomorphism in the complex analytic topology. [e]