algebraic geometry


algebraic geometry
a branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry.

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  • Algebraic geometry — This Togliatti surface is an algebraic surface of degree five. Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It… …   Wikipedia

  • algebraic geometry — Math. the study of sets that are defined by algebraic equations. [1895 1900] * * * Study of geometric objects expressed as equations and represented by graphs in a given coordinate system. In contrast to Euclidean geometry, algebraic geometry… …   Universalium

  • algebraic geometry — noun : analytic geometry in which the graphs or curves considered can be represented by algebraic equations * * * Math. the study of sets that are defined by algebraic equations. [1895 1900] …   Useful english dictionary

  • Algebraic Geometry (book) — Algebraic Geometry is an influential algebraic geometry textbook written by Robin Hartshorne and published by Springer Verlag in 1977. It was the first extended treatment of scheme theory written as a text intended to be accessible to graduate… …   Wikipedia

  • Algebraic geometry and analytic geometry — In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally… …   Wikipedia

  • Noncommutative algebraic geometry — is a branch of mathematics, and more specifically a direction in noncommutative geometry that studies the geometric properties of formal duals of non commutative algebraic objects such as rings as well as geometric objects derived from them (e.g …   Wikipedia

  • List of algebraic geometry topics — This is a list of algebraic geometry topics, by Wikipedia page. Contents 1 Classical topics in projective geometry 2 Algebraic curves 3 Algebraic surfaces 4 …   Wikipedia

  • Italian school of algebraic geometry — In relation with the history of mathematics, the Italian school of algebraic geometry refers to the work over half a century or more (flourishing roughly 1885 1935) done internationally in birational geometry, particularly on algebraic surfaces.… …   Wikipedia

  • Motive (algebraic geometry) — For other uses, see Motive (disambiguation). In algebraic geometry, a motive (or sometimes motif, following French usage) denotes some essential part of an algebraic variety . To date, pure motives have been defined, while conjectural mixed… …   Wikipedia

  • Divisor (algebraic geometry) — In algebraic geometry, divisors are a generalization of codimension one subvarieties of algebraic varieties; two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil). These… …   Wikipedia


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