coherent sheaf

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• 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

• Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia

• Sheaf spanned by global sections — In mathematics, a sheaf spanned by global sections is a sheaf F on a locally ringed space X , with structure sheaf O X that is of a rather simple type. Assume F is a sheaf of abelian groups. Then it is asserted that if A is the abelian group of… …   Wikipedia

• Coherent duality — In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the local… …   Wikipedia

• Sheaf cohomology — In mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F. This is the main step, in… …   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

• 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

• 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

• Ample line bundle — In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample. Globally… …   Wikipedia

• Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… …   Wikipedia