itself. Invertible sheaves are the invertible elements of this monoid. Specifically, if L is a sheaf of OX-modules, then L is called invertible if it satisfies...

module Invertible sheaf Invertible counterpoint Inverse (disambiguation) This disambiguation page lists articles associated with the title Invertible. If...

ample invertible sheaves states that if X is a quasi-compact quasi-separated scheme and L {\displaystyle {\mathcal {L}}} is an invertible sheaf on X,...

called the twisting sheaf of Serre. It can be checked that O ( 1 ) {\displaystyle {\mathcal {O}}(1)} is in fact an invertible sheaf. One reason for the...

E is a locally free sheaf of finite rank. In particular, if L is locally free of rank one (such L is called an invertible sheaf or a line bundle), then...

duality on V {\displaystyle V} . It may equally well be considered as an invertible sheaf. The canonical class is the divisor class of a Cartier divisor K {\displaystyle...

geometry. In algebraic geometry, the tautological line bundle (as invertible sheaf) is O P n ( − 1 ) , {\displaystyle {\mathcal {O}}_{\mathbb {P} ^{n}}(-1)...

O X ( n ) {\displaystyle {\mathcal {O}}_{X}(n)} is a line bundle (invertible sheaf) on X {\displaystyle X} and O X ( n ) {\displaystyle {\mathcal {O}}_{X}(n)}...

equivariant sheaf to be an equivariant object in the category of, say, coherent sheaves. A structure of an equivariant sheaf on an invertible sheaf or a line...

along s has degree r as an invertible sheaf over the fiber Xs (when the degree is defined for the Picard group of Xs.) Sheaf cohomology Chow variety Cartier...

Irrelevant ideal Locally ringed space Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch theorem...

{\displaystyle \pi ^{-1}{\mathcal {I}}\cdot {\mathcal {O}}_{\tilde {X}}} is an invertible sheaf, characterized by this universal property: for any morphism f: Y →...

fibrations of spheres to spheres. In algebraic geometry, an invertible sheaf (i.e., locally free sheaf of rank one) is often called a line bundle. Every line...

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

measured by the vanishing of the higher sheaf cohomology groups of the associated line bundle (formally, invertible sheaf). As the terminology reflects, this...

an invertible sheaf L is trivial if isomorphic to OX, as an OX-module. If the base X is a complex manifold, then an invertible sheaf is (the sheaf of...

be formulated in sheaf cohomology terms, as the non-vanishing of the H1 cohomology of the sheaf of sections of the invertible sheaf or line bundle associated...

Positivity of the line bundle L translates into the corresponding invertible sheaf being ample (i.e., some tensor power gives a projective embedding)...

divisors defining the embedding of V can be related to the line bundle or invertible sheaf defining the embedding by its space of sections. The tautological line...

logarithmic height h L {\displaystyle h_{L}} associated to a symmetric invertible sheaf L {\displaystyle L} on an abelian variety A {\displaystyle A} is “almost...

In mathematics, the gluing axiom is introduced to define what a sheaf F {\displaystyle {\mathcal {F}}} on a topological space X {\displaystyle X} must...

{\displaystyle {\mathcal {M}}_{X}.} Each Cartier divisor defines an invertible fractional ideal sheaf using the description of the Cartier divisor as a collection...

class as its dual. An explicit isogeny can be constructed by use of an invertible sheaf L on A (i.e. in this case a holomorphic line bundle), when the subgroup...

To see this, recall that for each divisor D on a curve there is an invertible sheaf O(D) (which corresponds to a line bundle) such that the linear system...

see this, recall that for each divisor D on a surface there is an invertible sheaf L = O(D) such that the linear system of D is more or less the space...

scheme is a scheme admitting an ample family of invertible sheaves. A scheme admitting an ample invertible sheaf is a basic example. dominant A morphism f :...

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...

giving rise to the projective embedding of V, such a line bundle (invertible sheaf) is said to be normally generated if V as embedded is projectively...

the n-th tensor power of the Serre twist sheaf O ( 1 ) {\displaystyle {\mathcal {O}}(1)} , the invertible sheaf or line bundle with associated Cartier divisor...

algebraic geometry, the equivalent definition is as an invertible sheaf, which squares to the sheaf of differentials of the first kind. Theta characteristics...