coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of...

especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties...

twisting sheaf on the Proj of a ring does. Let E {\displaystyle {\mathcal {E}}} be a quasi-coherent sheaf on a scheme X {\displaystyle X} . The sheaf of symmetric...

Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian...

In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module...

module spectrum. When the structure sheaf O X {\displaystyle {\mathcal {O}}_{X}} is not coherent, working with coherent sheaves has awkwardness (namely the...

notion of the coherent sheaf into algebraic geometry, that is, the notion of the coherent algebraic sheaf. The notion of coherent (coherent sheaf cohomology)...

a coherent sheaf F on a Stein manifold X. They are significant both as applied to several complex variables, and in the general development of sheaf cohomology...

sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology...

geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The...

Precisely, it is a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the rings of continuous...

In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf ω X {\displaystyle \omega _{X}} together...

ν. An analytic space is coherent if its structure sheaf O {\displaystyle {\mathcal {O}}} is a coherent sheaf. A coherent sheaf of O {\displaystyle {\mathcal...

bundle p : E → Y {\displaystyle p\colon E\to Y} (or more generally a coherent sheaf on Y) has a pullback to X, f ∗ E = { ( x , e ) ∈ X × E , f ( x ) = p...

the degree-zero subspace of a space of characters to the whole space Coherent sheaf, a specific class of sheaves having particularly manageable properties...

{\displaystyle {\mathcal {O}}_{X}} is coherent. Another important statement is as follows: For any coherent sheaf F {\displaystyle {\mathcal {F}}} on an...

quasi-coherent sheaf on a scheme X means an OX-module that is the sheaf associated to a module on each affine open subset of X. Finally, a coherent sheaf (on...

In mathematics, the stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. Sheaves are defined on open...

y]/(xy) are Cohen–Macaulay, but is not. coherent sheaf A coherent sheaf on a Noetherian scheme X is a quasi-coherent sheaf that is finitely generated as OX-module...

reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The second dual of a coherent sheaf is...

bundle gives way to that of a coherent sheaf. Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle...

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of...

geometry, a quasi-coherent sheaf on an algebraic stack X {\displaystyle {\mathfrak {X}}} is a generalization of a quasi-coherent sheaf on a scheme. The...

sheaves word for word. For example, the support of a coherent sheaf (or more generally, a finite type sheaf) is a closed subspace of X. If M is a module over...

Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch theorem Grothendieck–Riemann–Roch theorem Coherent...

In mathematics, the direct image functor is a construction in sheaf theory that generalizes the global sections functor to the relative case. It is of...

section. A slope of a vector bundle (or, more generally, a torsion-free coherent sheaf) E with respect to H is a rational number defined as μ ( E ) := c 1...

In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space P n {\displaystyle \mathbf {P} ^{n}} is the smallest...

prestack of quasi-coherent sheaves over a scheme S means that, for any S-scheme X, each X-point of the prestack is a quasi-coherent sheaf on X.) Theorem — The...

if X is a projective scheme over a Noetherian scheme S and if F is a coherent sheaf on X, then there is a scheme Quot F ⁡ ( X ) {\displaystyle \operatorname...