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...

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...

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...

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...

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

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

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...

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

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

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...

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

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...

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...

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...

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...

is the quasi-coherent sheaf of ideals cutting out Z, then the direct image i ∗ {\displaystyle i_{*}} from the category of quasi-coherent sheaves over...

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

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...

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...

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

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...

variety V that is non-singular it would be a global section of the coherent sheaf Ω1 of Kähler differentials. In either case the definition has its origins...

It is quasi-coherent if it is so as a module. When X is a scheme, just like a ring, one can take the global Spec of a quasi-coherent sheaf of algebras:...

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

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