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...

called the real projective line, which is topologically equivalent to a circle. RP2 is called the real projective plane. This space cannot be embedded...

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...

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

product space does not lie in its range and represents entangled states. Complex projective space Projective representation Projective space, for the...

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...

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space P n {\displaystyle \mathbb {P}...

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...

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...

resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exactly one point (there is no "parallel" case)...

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

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

real projective plane in which the "points" of the projective plane really are points. This means that the projective plane is the quotient space of the...

quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space of...

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

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...

Any field K {\displaystyle K} is a one-dimensional vector space over itself. The projective line over K , {\displaystyle K,} denoted P 1 ( K ) , {\displaystyle...

projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space...

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

as hyperbolic space. A further classical example is the space of lines in projective space of three dimensions (equivalently, the space of two-dimensional...

of real and complex projective space. Therefore the classifying space BC2 is of the homotopy type of RP∞, the real projective space given by an infinite...

isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space. In terms of matrices,...

In 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...

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...

can vanish at a point of projective space. The projective Nullstellensatz gives a bijective correspondence between projective varieties and homogeneous...

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]...

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

geometry may be defined as a projective space over a finite field. Objects of study include affine and projective spaces over finite fields and various...