In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X, the relative Spec C = Spec X ⁡ R {\displaystyle C=\operatorname...

In algebraic geometry, the normal cone of a subscheme of a scheme is a scheme analogous to the normal bundle or tubular neighborhood in differential geometry...

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

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

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...

Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and...

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

toric algebraic geometry, combinatorial commutative algebra, geometric combinatorics, integer programming.". This object arises when we study cones in R...

pseudo-Euclidean) space with a null cone added at infinity". That is, the setting is a compactification of a familiar space; the geometry is concerned with the implications...

In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the...

In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities. In...

early geometry. (See Areas of mathematics and Algebraic geometry.) The earliest recorded beginnings of geometry can be traced to early peoples, such as the...

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in...

reconstructed from the Banach algebra of functions on the space (Gelfand–Naimark). In commutative algebraic geometry, algebraic schemes are locally prime...

foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system...

In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric...

as π that are not algebraic are said to be transcendental. Almost all real and complex numbers are transcendental. Algebraic geometry is a branch of mathematics...

topological spaces. Bicone Cone (linear algebra) Cylinder (geometry) Democritus Generalized conic Hyperboloid List of shapes Pyrometric cone Quadric Rotation of...

In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X {\displaystyle X} is a combinatorial invariant of importance...

space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry and to describe some basic...

commutative affine algebraic group commonly found in projective algebraic geometry and toric geometry. Higher dimensional algebraic tori can be modelled...

equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than...

definition of vector spaces as an algebraic structure. In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional...

In topology, especially algebraic topology, the cone of a topological space X {\displaystyle X} is intuitively obtained by stretching X into a cylinder...

some axioms (such as Playfair's axiom). Affine geometry can also be developed on the basis of linear algebra. In this context an affine space is a set of...

analytic geometry, introduced almost 2,000 years later by René Descartes, which uses coordinates to express geometric properties by means of algebraic formulas...

} The null cone is also the union of the isotropic lines through the origin. A composition algebra with a null vector is a split algebra. In a composition...

implies x ∈ I {\displaystyle x\in I} . Both notions are important in algebraic geometry, because of Hilbert's Nullstellensatz. An element of a ring that is...

considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property). This article...

term "algebraic statistics" has been sometimes restricted, sometimes being used to label the use of algebraic geometry and commutative algebra in statistics...