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Longer titles found: Gromov's inequality for complex projective space (view)

searching for Complex projective space 34 found (153 total)

alternate case: complex projective space

Twistor string theory (316 words) [view diff] exact match in snippet view article find links to article

quantum theory with gravity. Twistor space is a three-dimensional complex projective space in which physical quantities appear as certain structural deformations

Serre spectral sequence (2,641 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {Z} [x]/x^{n+1}.} In the case of infinite complex projective space, taking limits gives the answer Z [ x ] . {\displaystyle \mathbb

Homotopy group (3,432 words) [view diff] no match in snippet view article find links to article

In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental

Fermat quintic threefold (310 words) [view diff] exact match in snippet view article find links to article

other words a degree 5, dimension 3 hypersurface in 4-dimensional complex projective space, given by the equation V 5 + W 5 + X 5 + Y 5 + Z 5 = 0 {\displaystyle

Symmetric product of an algebraic curve (582 words) [view diff] exact match in snippet view article find links to article

{∞} ≈ S2), its nth symmetric product ΣnC can be identified with complex projective space C P n {\displaystyle \mathbb {CP} ^{n}} of dimension n. If G has

Pierre Lelong (357 words) [view diff] exact match in snippet view article find links to article

inside a complex projective space and there are many complex- analytic objects on it which are constructed from those on the complex projective space. When

Grassmann bundle (520 words) [view diff] exact match in snippet view article find links to article

{P} (V)} ), there is the natural identification (see Chern class#Complex projective space for example): Hom ⁡ ( l , V / l ) = T l P ( V ) {\displaystyle

Abelian variety (3,158 words) [view diff] exact match in snippet view article find links to article

those complex tori that can be holomorphically embedded into a complex projective space. Abelian varieties defined over algebraic number fields are a special

Complex affine space (2,538 words) [view diff] exact match in snippet view article find links to article

projective geometry. A complex affine space can be obtained from a complex projective space by fixing a hyperplane, which can be thought of as a hyperplane

Simple Lie group (2,379 words) [view diff] exact match in snippet view article find links to article

PUSp(n), PUSp(2n) Hermitian. Complex structures of Hn. Copies of complex projective space in quaternionic projective space. Dn (n ≥ 4) compact n(2n − 1)

Line bundle (1,885 words) [view diff] exact match in snippet view article find links to article

explicitly, in the infinite-dimensional analogues of real and complex projective space. Therefore the classifying space B C 2 {\displaystyle BC_{2}} is

Richard S. Ward (441 words) [view diff] exact match in snippet view article find links to article

describe instantons by vector bundles on the three-dimensional complex projective space. He has related interests in the theory of monopoles, topological

Algebraic geometry and analytic geometry (2,782 words) [view diff] exact match in snippet view article find links to article

of comparison available. It states that an analytic subspace of complex projective space that is closed (in the ordinary topological sense) is an algebraic

Classifying space (1,893 words) [view diff] exact match in snippet view article find links to article

symmetric group S n . {\displaystyle S_{n}.} The infinite dimensional complex projective space C P ∞ {\displaystyle \mathbb {CP} ^{\infty }} is the classifying

Mark Lee Green (554 words) [view diff] exact match in snippet view article find links to article

American Mathematical Society in 2012. "Holomorphic maps into complex projective space omitting hyperplanes." Transactions of the American Mathematical

Welch bounds (1,389 words) [view diff] exact match in snippet view article find links to article

if the set of vectors is a t {\displaystyle t} -design in the complex projective space C P n − 1 {\displaystyle \mathbb {CP} ^{n-1}} . Spherical design

Jumping line (519 words) [view diff] exact match in snippet view article find links to article

skew-symmetric form. There is a rank 2 vector bundle over the 3-dimensional complex projective space associated to V, that assigns to each line L of V the 2-dimensional

Continuous geometry (1,514 words) [view diff] exact match in snippet view article find links to article

elements with unique complements are 0 and 1. Finite-dimensional complex projective space, or rather its set of linear subspaces, is a continuous geometry

Linear fractional transformation (1,703 words) [view diff] exact match in snippet view article find links to article

flow induced by the linear fractional transformation decomposes complex projective space into stable and unstable manifolds, with the horocycles appearing

Geometric invariant theory (2,272 words) [view diff] exact match in snippet view article find links to article

so that non-zero orbits are parametrized by the points of the complex projective space CPn–1. If this happens (different orbits having the same function

Ovoid (projective geometry) (1,520 words) [view diff] exact match in snippet view article

(projective space over C {\displaystyle {\mathbb {C} }} ). In a complex projective space of dimension d ≥ 3 there are no ovoidal quadrics, because in that

Cotangent sheaf (891 words) [view diff] exact match in snippet view article find links to article

{\mathcal {O}}_{\mathbf {P} _{R}^{n}}\to 0.} (See also Chern class#Complex projective space.) For this notion, see § 1 of A. Beilinson and V. Drinfeld, Quantization

4-manifold (3,662 words) [view diff] exact match in snippet view article find links to article

depending on the Kirby–Siebenmann invariant: one is 2-dimensional complex projective space, and the other is a fake projective space, with the same homotopy

Projective orthogonal group (1,874 words) [view diff] exact match in snippet view article find links to article

while PU preserves a hermitian form – PU is the symmetries of complex projective space (preserving the Fubini–Study metric). In fields of characteristic

Riemann–Roch theorem (4,966 words) [view diff] exact match in snippet view article find links to article

compact Riemann surface is defined by algebraic equations in some complex projective space. (Chow's Theorem says that any closed analytic subvariety of projective

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

x_{n}} simultaneously vanish. Let Pn - 1 be (n - 1)-dimensional complex projective space with homogeneous coordinates y 1 , … , y n {\displaystyle y_{1}

Carlos Benjamin de Lyra (2,522 words) [view diff] exact match in snippet view article find links to article

167-184. Lyra, Carlos Benjamin de (1959). "On circle bundles over complex projective space". Anais da Academia Brasileira de Ciências. Vol. 31, no. 1. p. 17-24

Algebraic curve (7,993 words) [view diff] exact match in snippet view article find links to article

A complex projective algebraic curve resides in n-dimensional complex projective space CPn. This has complex dimension n, but topological dimension, as

Sylvester–Gallai theorem (5,243 words) [view diff] exact match in snippet view article find links to article

points of a Sylvester–Gallai configuration are embedded into a complex projective space, the points must all lie in a two-dimensional subspace. Equivalently

Michael Atiyah (8,832 words) [view diff] exact match in snippet view article find links to article

to give a cobordism between the manifold and a sum of copies of complex projective space. He deduced from this that the intersection form must be a sum

Divisor (algebraic geometry) (6,612 words) [view diff] exact match in snippet view article

smooth complete intersection variety of dimension at least 3 in complex projective space, then the Picard group of Y is isomorphic to Z, generated by the

Lorentz group (9,875 words) [view diff] exact match in snippet view article find links to article

sits on the unit sphere. From the Möbius side, SL(2, C) acts on complex projective space CP1, which can be shown to be diffeomorphic to the 2-sphere – this

Surgery exact sequence (3,121 words) [view diff] exact match in snippet view article find links to article

to n ≥ 1 {\displaystyle n\geq 1} by some ad-hoc methods.) The complex projective space C P n {\displaystyle \mathbb {C} P^{n}} is a ( 2 n ) {\displaystyle

Glossary of classical algebraic geometry (11,193 words) [view diff] exact match in snippet view article find links to article

such as "circle", have their meanings tacitly changed to work in complex projective space; for example, a circle in complex algebraic geometry is a conic