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searching for Projectivization 36 found (47 total)

Plücker embedding (1,332 words) [view diff] exact match in snippet view article find links to article

map embeds G r ( k , V ) {\displaystyle \mathrm {Gr} (k,V)} into the projectivization P ( ⋀ k V ) {\displaystyle \mathbb {P} ({\textstyle \bigwedge }^{k}V)}

Finite geometry (2,841 words) [view diff] exact match in snippet view article find links to article

isomorphic to a projective space over a finite field (that is, the projectivization of a vector space over a finite field). However, dimension two has

Algebraic geometry of projective spaces (1,400 words) [view diff] exact match in snippet view article find links to article

over k defined by Proj(k[V]) is called projectivization of V. The projective n-space on k is the projectivization of the vector space A k n + 1 {\displaystyle

Contact geometry (2,527 words) [view diff] exact match in snippet view article find links to article

some of dimension 2n − 1, some of dimension 2n + 1. Projectivization Let M be the projectivization of the cotangent bundle of N: thus M is fiber bundle

Pure spinor (2,923 words) [view diff] exact match in snippet view article find links to article

irreducible spinor (or half-spinor) modules. Pure spinors, defined up to projectivization, are called projective pure spinors. For V {\displaystyle \,V\,} of

Grassmannian (8,402 words) [view diff] exact match in snippet view article find links to article

Grassmannian G r ( k , V ) {\displaystyle \mathbf {Gr} (k,V)} into the projectivization of the k {\displaystyle k} th Exterior power Λ k V {\displaystyle \Lambda

Algebraic combinatorics (1,289 words) [view diff] exact match in snippet view article find links to article

isomorphic to a projective space over a finite field (that is, the projectivization of a vector space over a finite field). However, dimension two has

Hirzebruch surface (1,693 words) [view diff] exact match in snippet view article find links to article

of line bundles on P 1 {\displaystyle \mathbb {P} ^{1}} and their projectivization. For the direct sum O ⊕ O ( − n ) {\displaystyle {\mathcal {O}}\oplus

Projective polyhedron (2,111 words) [view diff] exact match in snippet view article find links to article

dimensions are as follows: n-dimensional real projective space is the projectivization of (n+1)-dimensional Euclidean space, R P n = P ( R n + 1 ) , {\displaystyle

Cayley plane (412 words) [view diff] exact match in snippet view article find links to article

group E6 by a parabolic subgroup P1. It is the closed orbit in the projectivization of the minimal complex representation of E6. The complex Cayley plane

Projective linear group (5,613 words) [view diff] exact match in snippet view article find links to article

exception of the non-Desarguesian planes, all projective spaces are the projectivization of a linear space over a division ring though, as noted above, there

Julius Plücker (1,046 words) [view diff] exact match in snippet view article find links to article

Grassmannian G r ( k , V ) {\displaystyle \mathbf {Gr} (k,V)} into the projectivization P ( Λ k ( V ) ) {\displaystyle \mathbf {P} (\Lambda ^{k}(V))} of the

Cayley–Bacharach theorem (1,492 words) [view diff] exact match in snippet view article find links to article

curve of degree d is the number of monomials of degree d, minus 1 from projectivization. For the first few d these yield: d = 1: 2 and 1: two points determine

Tropical projective space (360 words) [view diff] exact match in snippet view article find links to article

projective space. Given a module M over the tropical semiring T, its projectivization is the usual projective space of a module: the quotient space of the

Blowing up (4,260 words) [view diff] exact match in snippet view article find links to article

{m}}=(x,y)} is the maximal ideal of the origin. Algebraically, the projectivization of this vector space is Proj of its symmetric algebra, that is, X =

Projective plane (6,933 words) [view diff] exact match in snippet view article find links to article

outlined above, used to obtain it, is called "projective completion" or projectivization. This plane can also be constructed by starting from R3 viewed as a

Covering group (1,731 words) [view diff] exact match in snippet view article find links to article

group of scalar matrices, and thus the group mod its center is the projectivization of the Lie group. These covers are important in studying projective

Projective bundle (1,373 words) [view diff] exact match in snippet view article find links to article

2-cocycle which vanishes in H2(X,O*) only if the projective bundle is the projectivization of a vector bundle. In particular, if X is a compact Riemann surface

Index of a subgroup (2,612 words) [view diff] exact match in snippet view article find links to article

third. This is a simple corollary of the above discussion (namely the projectivization of the vector space structure of the elementary abelian group G / E

Translation surface (4,595 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathbb {C} }^{*}} -action and thus a real and complex projectivization H ( α ) → H 1 ( α ) → H 2 ( α ) {\displaystyle {{\mathcal {H}}(\alpha

Brauer group (2,937 words) [view diff] exact match in snippet view article find links to article

is defined to be zero in the Brauer group if and only if it is the projectivization of some vector bundle. The cohomological Brauer group of a quasi-compact

Pin group (2,502 words) [view diff] exact match in snippet view article find links to article

PO(2), though in this case it is also realized geometrically, as "the projectivization of a 2n-gon in the circle is an n-gon in the projective line". In 3

Five points determine a conic (2,331 words) [view diff] exact match in snippet view article find links to article

{n+1 \choose d}\!\!\right)},} from which 1 is subtracted because of projectivization: multiplying a polynomial by a constant does not change its zeros.

Linear system of divisors (2,910 words) [view diff] exact match in snippet view article find links to article

{\displaystyle V=\Gamma ({\mathcal {O}}(d))} , then we can take its projectivization P ( V ) {\displaystyle \mathbb {P} (V)} . This is isomorphic to P N

Huai-Dong Cao (1,739 words) [view diff] exact match in snippet view article find links to article

closed examples of gradient shrinking Kähler-Ricci solitons on the projectivization of certain line bundles over complex projective space; these examples

Integrable system (3,407 words) [view diff] exact match in snippet view article find links to article

relations, characterizing the Plücker embedding of the Grassmannian in the projectivization of a suitably defined (infinite) exterior space, viewed as a fermionic

Chow variety (2,177 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {P} ^{n-1}} of dimension k-1 and degree 1 is the projectivization of a k-dimensional subspace of n-dimensional affine space. This gives

Tau function (integrable systems) (6,689 words) [view diff] exact match in snippet view article

the Fock space F 0 {\displaystyle {\mathcal {F}}_{0}} which, up to projectivization, is the image of the Grassmannian element w ∈ G r H + ( H ) {\displaystyle

Hilbert scheme (3,409 words) [view diff] exact match in snippet view article find links to article

hypersurfaces in P n {\displaystyle \mathbb {P} ^{n}} is given by the projectivization P ( Γ ( O ( k ) ) ) {\displaystyle \mathbb {P} (\Gamma ({\mathcal {O}}(k)))}

Chern class (7,508 words) [view diff] exact match in snippet view article find links to article

class of a tautologically-defined line bundle. Namely, introducing the projectivization P ( E ) {\displaystyle \mathbb {P} (E)} of the rank n complex vector

Cross-ratio (4,844 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathrm {PGL} (n,K)=\mathbf {P} (\mathrm {GL} (n+1,K)),} projectivization removing one dimension), but in other dimensions the projective linear

Quartic function (6,853 words) [view diff] exact match in snippet view article find links to article

quadratics (a pencil of curves) passing through these points. Writing the projectivization of the two quadratics as quadratic forms in three variables: F 1 (

Hilbert space (17,469 words) [view diff] exact match in snippet view article find links to article

phase factor). In other words, the possible states are points in the projectivization of a Hilbert space, usually called the complex projective space. The

Lie sphere geometry (3,959 words) [view diff] exact match in snippet view article find links to article

(projective) line lying entirely on the Lie quadric, i.e., it is the projectivization of a totally null two dimensional subspace of R 3,2: the representative

Outer space (mathematics) (4,144 words) [view diff] exact match in snippet view article

actions coincide, so the closure can be understood in either sense. The projectivization of c v ¯ n {\displaystyle {\overline {cv}}_{n}} with respect to multiplication

Valuation (geometry) (5,983 words) [view diff] exact match in snippet view article

the co-sphere bundle of X , {\displaystyle X,} that is, the oriented projectivization of the cotangent bundle. Let P ( X ) {\displaystyle {\mathcal {P}}(X)}