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...

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...

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,...

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

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...

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

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...

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...

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...

{\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...

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

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

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

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...

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)}...

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...

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...

calculated by homological algebra means, from a minimal resolution of an invertible sheaf of high degree. In many cases the gonality is two more than the Clifford...

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...

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...

theorem proved by Mumford in 1967 states that if L is a semi-ample invertible sheaf with Iitaka dimension at least 2 on a complex projective manifold,...

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...

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

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 :...

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...

A^{i}(X)} such that c 0 ( E ) = 1 {\displaystyle c_{0}(E)=1} For an invertible sheaf O X ( D ) {\displaystyle {\mathcal {O}}_{X}(D)} (so that D {\displaystyle...