mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle if it...
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of projective space the tautological bundle is known as the tautological line bundle. The tautological bundle is also called the universal bundle since...
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a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative"...
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K-theory (section K0 of a projective bundle)
tangent bundle of an intersection of spaces: Let Y 1 , Y 2 ⊂ X {\displaystyle Y_{1},Y_{2}\subset X} be projective subvarieties of a smooth projective variety...
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complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...
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In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in...
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real projective line, which is topologically equivalent to a circle. R P 2 {\displaystyle \mathbb {RP} ^{2}} is called the real projective plane...
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_{n}} is the P 1 {\displaystyle \mathbb {P} ^{1}} -bundle (a projective bundle) over the projective line P 1 {\displaystyle \mathbb {P} ^{1}} , associated...
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canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle...
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Chow group (section Projective bundle formula)
group of line bundles on X {\displaystyle X} . Rationally equivalent cycles defined by hypersurfaces are easy to construct on projective space because...
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Euler sequence (category Projective geometry)
sheaf. The Euler sequence generalizes to that of a projective bundle as well as a Grassmann bundle (see the latter article for this generalization.) Let...
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Cone (algebraic geometry) (redirect from Projective completion of a cone)
written just as E, and the projective cone Proj X R {\displaystyle \operatorname {Proj} _{X}R} is the projective bundle of E, which is written as P...
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bundle I-bundle Natural bundle Principal bundle Projective bundle Pullback bundle Quasifibration Universal bundle Vector bundle Wu–Yang dictionary Seifert...
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bundle comes from a divisor. (II) If X {\displaystyle X} is projective scheme then the same statement holds. One of the most important line bundles in...
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concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...
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Moduli space (redirect from Moduli of vector bundles)
{\displaystyle d} hypersurfaces of projective space P n {\displaystyle \mathbb {P} ^{n}} . This is given by the projective bundle H i l b d ( P n ) = P ( Γ (...
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\mathbb {Z} _{2}} -bundle over S 1 {\displaystyle S^{1}} . Projective spaces provide some more interesting examples of principal bundles. Recall that the...
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classifying spaces for vector bundle, among which projective spaces for line bundles Characteristic class Splitting principle Stable bundle Connection: the notion...
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Hopf fibration (redirect from Hopf bundle)
fibers over real projective space RPn with fiber S0. The Hopf construction gives circle bundles p : S2n+1 → CPn over complex projective space. This is actually...
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n-dimensional linear system of divisors on a line bundle on X. The choice of a projective embedding of X, modulo projective transformations is likewise equivalent...
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Coherent sheaf (redirect from Vector bundle over a ringed space)
tangent bundle of projective space P n {\displaystyle \mathbb {P} ^{n}} over a field k {\displaystyle k} can be described in terms of the line bundle O (...
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Glossary of algebraic geometry (redirect from Projective morphism)
open subscheme of a projective space P A n {\displaystyle \mathbb {P} _{A}^{n}} over a ring A {\displaystyle A} . projective bundle If E is a locally free...
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{\displaystyle |D|} is therefore a projective space. A linear system d {\displaystyle {\mathfrak {d}}} is then a projective subspace of a complete linear system...
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especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action...
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the projective bundle of E. In the other direction, a Grassmann bundle is a special case of a (partial) flag bundle. Concretely, the Grassmann bundle can...
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Proj construction (section Projective space bundles)
schemes, which produces objects with the typical properties of projective spaces and projective varieties. The construction, while not functorial, is a fundamental...
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using either Azumaya algebras over X or projective bundles over X. The second definition involves projective bundles that are locally trivial in the étale...
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the property of lifting that carries over from free to projective modules: a module P is projective if and only if for every surjective module homomorphism...
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In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates...
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geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described...
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