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In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).
In rhetoric, a scheme is a type of figure of speech that relies on the structure of the sentence, unlike the trope, which plays with the meanings of words. [ 1 ] A single phrase may involve both a trope and a scheme, e.g., may use both alliteration and allegory .
A rhyme scheme is the pattern of rhymes at the end of each line of a poem or song. It is usually referred to by using letters to indicate which lines rhyme; lines designated with the same letter all rhyme with each other. An example of the ABAB rhyming scheme, from "To Anthea, who may Command him Anything", by Robert Herrick:
An example of a singular (non-smooth) scheme over a field k is the closed subscheme x 2 = 0 in the affine line A 1 over k. An example of a singular (non-smooth) variety over k is the cuspidal cubic curve x 2 = y 3 in the affine plane A 2, which is smooth outside the origin (x,y) = (0,0).
Scheme is a dialect of the Lisp family of programming languages.Scheme was created during the 1970s at the MIT Computer Science and Artificial Intelligence Laboratory (MIT CSAIL) and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers.
Fix a scheme S, called a base scheme. Then a morphism : is called a scheme over S or an S-scheme; the idea of the terminology is that it is a scheme X together with a map to the base scheme S. For example, a vector bundle E → S over a scheme S is an S-scheme.
(A Hilbert scheme is a scheme rather than a stack, because, very roughly speaking, deformation theory is simpler for closed schemes.) Some moduli problems are solved by giving formal solutions (as opposed to polynomial algebraic solutions) and in that case, the resulting functor is represented by a formal scheme .
A pyramid scheme is a business model which, rather than earning money ... (1 + 2 + 4 + 8) in the scheme—with the Airplane Game as the example, the person at the top ...