- ideal sheaf
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English-Russian scientific dictionary. 2008.
ideal sheaf
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Ideal sheaf — In algebraic geometry and other areas of mathematics, an ideal sheaf (or sheaf of ideals) is the global analogue of an ideal in a ring. The ideal sheaves on a geometric object are closely connected to its subspaces. Definition Let X be a… … Wikipedia
Coherent sheaf — In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space … Wikipedia
Stalk (sheaf) — The stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point.Motivation and definitionSheaves are defined on open sets, but the underlying topological space X consists of points. It is reasonable to… … Wikipedia
Invertible sheaf — In mathematics, an invertible sheaf is a coherent sheaf S on a ringed space X , for which there is an inverse T with respect to tensor product of O X modules. That is, we have : S otimes; T isomorphic to O X , which acts as identity element for… … Wikipedia
Holomorphic sheaf — In mathematics, more specifically complex analysis, a holomorphic sheaf (often also called an analytic sheaf) is a natural generalization of the sheaf of holomorphic functions on a complex manifold. DefinitionIt takes a rather involved string of… … Wikipedia
Multiplier ideal — In commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number c consists (locally) of the functions h such that is locally integrable, where the fi are a finite set of local generators of… … Wikipedia
Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… … 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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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
Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… … Wikipedia
