# Algebraic geometry/Related Articles

From Citizendium, the Citizens' Compendium

*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.
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