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 and...

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...

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...

algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals...

Italian school of algebraic geometry that the complex projective spaces were the most natural domains in which to consider the solutions of polynomial equations...

space of dimension 1 is a projective line, and a projective space of dimension 2 is a projective plane. Projective spaces are widely used in geometry, allowing...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective planes...

of Translation Planes from Projective Spaces" (PDF), J. Algebra, 1: 85–102, doi:10.1016/0021-8693(64)90010-9 Casse, Rey (2006), Projective Geometry:...

specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or...

Euclidean spaces are affine spaces, and that these kinds of projections are fundamental in Euclidean geometry. More precisely, given an affine space E with...

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...

history of mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces...

manifolds or projective complex algebraic varieties. Complex geometry is different in flavour to what might be called real geometry, the study of spaces based...

topological spaces can be reconstructed from the Banach algebra of functions on the space (Gelfand–Naimark). In commutative algebraic geometry, algebraic schemes...

is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For...

of algebraic geometry is built in complex affine spaces and affine spaces over algebraically closed fields. The shapes that are studied in algebraic geometry...

algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a...

fundamental variety was projective space. The geometry of projective space is closely related to the theory of perspective, and its algebra is described by homogeneous...

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast...

generalization of projective linear maps. The projective line is a fundamental example of an algebraic curve. From the point of view of algebraic geometry, P1(K)...

application is the blow-up of a scheme with respect to a coherent sheaf of ideals. Projective space Algebraic geometry of projective spaces Projectivization Ravi...

units of length (e.g., metre). In algebraic geometry there are several structures that are one-dimensional spaces but are usually referred to by more...

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called...

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

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside...

is the solution of a single linear equation. Projective hyperplanes, are used in projective geometry. A projective subspace is a set of points with the...