point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be...

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 label...

In mathematics, real projective space, denoted ⁠ R P n {\displaystyle \mathbb {RP} ^{n}} ⁠ or ⁠ P n ( R ) , {\displaystyle \mathbb {P} _{n}(\mathbb {R}...

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...

mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates...

space. In quantum mechanics, the equivalence classes [ v ] {\displaystyle [v]} are also referred to as rays or projective rays. Each such projective ray...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry. A projective plane C may be defined axiomatically...

real projective plane, denoted ⁠ R P 2 {\displaystyle \mathbf {RP} ^{2}} ⁠ or ⁠ P 2 {\displaystyle \mathbb {P} _{2}} ⁠, is a two-dimensional projective space...

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...

compared to elementary Euclidean geometry, projective geometry has a different setting (projective space) and a selective set of basic geometric concepts...

subsets of projective space. Projective varieties were subsets defined by a set of homogeneous polynomials. At each point of the projective variety, all...

In algebraic geometry, a weighted projective space P(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn]...

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces...

line, called a projective line. Dimension 2: There are at least 2 lines, and any two lines meet. A projective space for n = 2 is a projective plane. These...

In projective geometry and mathematics more generally, a projective line is, roughly speaking, the extension of a usual line by a point called a point...

rational over the Gaussian rationals. A projective (algebraic) hypersurface of dimension n – 1 in a projective space of dimension n over a field k is defined...

and more specifically in projective geometry, a projective frame or projective basis is a tuple of points in a projective space that can be used for defining...

In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...

The concept of a Projective space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry...

by definition quasi-projective varieties, meaning that they were open subvarieties of closed subvarieties of a projective space. For example, in Chapter...

projective space Pn is a moduli space that parametrizes the space of lines in Rn+1 which pass through the origin. Similarly, complex projective space...

homogeneous coordinates in the traditional sense of projective geometry. The Betti numbers of the complex projective plane are 1, 0, 1, 0, 1, 0, 0, ..... The middle...

tautological line bundle on projective space. The projectivization P ( V ) {\displaystyle \mathbf {P} (V)} of a vector space V {\displaystyle V} over a...

defining a projective space as the set of the vector lines in a vector space of dimension one more. As for affine spaces, projective spaces are defined...

group is a subgroup of the projective group. For instance, Möbius transformations (transformations of the complex projective line, or Riemann sphere) are...

schemes, which produces objects with the typical properties of projective spaces and projective varieties. The construction, while not functorial, is a fundamental...

isomorphic to it. There are exactly 50 fake projective planes. Prasad & Yeung (2006) found four examples of fake projective 4-folds, and showed that no arithmetic...

itself. The projective line over K , {\displaystyle K,} denoted P 1 ( K ) , {\displaystyle \mathbf {P} ^{1}(K),} is a one-dimensional space. In particular...

points of the projective completion are the points of the projective space whose projective coordinates are zeros of P. So, a projective quadric is the...