- algebraic variety
- мат. алгебраическое многообразие
Большой англо-русский и русско-английский словарь. 2001.
Большой англо-русский и русско-английский словарь. 2001.
Algebraic variety — This article is about algebraic varieties. For the term a variety of algebras , and an explanation of the difference between a variety of algebras and an algebraic variety, see variety (universal algebra). The twisted cubic is a projective… … Wikipedia
Abstract algebraic variety — In algebraic geometry, an abstract algebraic variety is an algebraic variety that is defined intrinsically, that is, without an embedding into another variety.In classical algebraic geometry, all varieties were by definition quasiprojective… … Wikipedia
Function field of an algebraic variety — In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V . In complex algebraic geometry these are meromorphic functions and their higher dimensional analogues; in… … Wikipedia
Singular point of an algebraic variety — In mathematics, a singular point of an algebraic variety V is a point P that is special (so, singular), in the geometric sense that V is not locally flat there. In the case of an algebraic curve, a plane curve that has a double point, such as the … Wikipedia
Complete algebraic variety — In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphism X × Y → Y is a closed map, i.e. maps closed sets onto closed sets.[1] The most common … Wikipedia
Dimension of an algebraic variety — In mathematics, the dimension of an algebraic variety V in algebraic geometry is defined, informally speaking, as the number of independent rational functions that exist on V. For example, an algebraic curve has by definition dimension 1. That… … Wikipedia
Degree of an algebraic variety — The degree of an algebraic variety in mathematics is defined, for a projective variety V, by an elementary use of intersection theory. For V embedded in a projective space Pn and defined over some algebraically closed field K, the degree d of V… … Wikipedia
Variety — may refer to: *Variety (botany), a rank in botany below that of species. *Variety (cybernetics), the number of possible states of a system or of an element of the system. *Variety (linguistics), a concept that includes for instance dialects,… … Wikipedia
Algebraic statistics — is a fairly recent field of statistics which utilizes the tools of algebraic geometry and commutative algebra in order to study problems related to discrete random variables with finite state spaces. Such problems include parameter estimation,… … Wikipedia
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
Variety (universal algebra) — This article is about a class of algebraic structures of the same signature. For the set of solutions to a system of polynomial equations, see Algebraic variety. In mathematics, specifically universal algebra, a variety of algebras is the class… … Wikipedia