Web3 Apr 2024 · A coherent subsheaf F of some sheaf G is said to be saturated in G if the quotient sheaf G / F is torsion-free. Further, we can define the saturation of F inside G to … Web1 Jan 1973 · Every locally finitely generated subsheaf of coherent. d 167 p is Proof. This is just another way of stating the Oka theorem (Theorem 6.4.1). In particular, d p a coherent analytic sheaf, and so is the sheaf of is germs of analytic sections of an analytic vector bundle. Theorem 7.1.6.
Lemma 17.12.4 (01BY)—The Stacks project - Columbia University
Broadly speaking, coherent sheaf cohomology can be viewed as a tool for producing functions with specified properties; sections of line bundles or of more general sheaves can be viewed as generalized functions. In complex analytic geometry, coherent sheaf cohomology also plays a foundational role. See more In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of … See more On an arbitrary ringed space quasi-coherent sheaves do not necessarily form an abelian category. On the other hand, the quasi-coherent sheaves on any scheme form an abelian category, and they are extremely useful in that context. On any ringed space See more Let $${\displaystyle f:X\to Y}$$ be a morphism of ringed spaces (for example, a morphism of schemes). If $${\displaystyle {\mathcal {F}}}$$ is a quasi-coherent sheaf on $${\displaystyle Y}$$, then the inverse image If See more For a morphism of schemes $${\displaystyle X\to Y}$$, let $${\displaystyle \Delta :X\to X\times _{Y}X}$$ be the diagonal morphism, which is a closed immersion if $${\displaystyle X}$$ is separated over $${\displaystyle Y}$$. Let See more A quasi-coherent sheaf on a ringed space $${\displaystyle (X,{\mathcal {O}}_{X})}$$ is a sheaf $${\displaystyle {\mathcal {F}}}$$ of $${\displaystyle {\mathcal {O}}_{X}}$$-modules which has a local presentation, that is, every point in $${\displaystyle X}$$ has … See more • An $${\displaystyle {\mathcal {O}}_{X}}$$-module $${\displaystyle {\mathcal {F}}}$$ on a ringed space $${\displaystyle X}$$ is called locally free of finite rank, or a vector bundle, … See more An important feature of coherent sheaves $${\displaystyle {\mathcal {F}}}$$ is that the properties of $${\displaystyle {\mathcal {F}}}$$ at … See more Websentation is what we call the Noether-Lasker decomposition of the coherent analytic subsheaf. If (X, is Stein, then a coherent analytic proper subsheaf .9 of a coherent analytic sheaf SY is primary if and only if F(X, Y) is a primary submodule of the F(X, ()-module r(X, Y). The Noether-Lasker decomposition of subsheaves is derived from the gap- batch edit mp3 metadata
Extension of Coherent Analytic Subsheaves* - Springer
Web6 Jan 2024 · A classical special case is the sheaf $\cO$ of germs of holomorphic functions in a domain of $\mathbf C^n$; the statement that it is coherent is known as the Oka … Web31 Jan 2024 · I'm trying to deal with an example of a rank two vector bundle over the complex projective plane which is non slope-stable (because the associated sheaf of sections has a coherent subsheaf of equal slope) but … WebA coherent sheaf E on P2 is Gieseker semistable (respectively stable) if E is of pure dimension (that is, every nonzero subsheaf of E has a support of dimension equal to the dimension of the support of E), and, for every nonzero strict subsheaf F of E, we have p F(n)Dp E(n) (respectively p F(n) batch duden