In algebraic geometry, a geometric quotient of an algebraic variety X with the action of an algebraic group G is a morphism of varieties π : X → Y {\displaystyle...

In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme X = Spec ⁡ A {\displaystyle X=\operatorname...

In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli...

{\displaystyle E/k} . geometric quotient The geometric quotient of a scheme X with the action of a group scheme G is a good quotient such that the fibers...

main motivations for the development of geometric invariant theory was the construction of a categorical quotient for varieties or schemes. Note π {\displaystyle...

algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety...

A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by...

In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant...

X is geometric if it satisfies the following conditions: Each element of G acts as an isometry of X. The action is cocompact, i.e. the quotient space...

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let h ( x ) = f (...

reaches its mean value at some point in the interval. Geometrically, this difference quotient measures the slope of the secant line passing through the...

algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra...

to Y. This gives a way to visualize quotient spaces geometrically. (By re-parameterising these lines, the quotient space can more conventionally be represented...

given by the ideal quotient ( ( 1 ) : I ) = I − 1 {\displaystyle ((1):I)=I^{-1}} . One geometric application of the ideal quotient is removing an irreducible...

symplectic quotient construction. By the Kempf-Ness theorem, a Kähler quotient by a compact Lie group G {\displaystyle G} is closely related to a geometric invariant...

nearby points. Branched covering Euler characteristic of an orbifold Geometric quotient Kawasaki's Riemann–Roch formula Orbifold notation Orientifold Ring...

object together with a level structure Geometric invariant theory - throw away bad orbits and then take a quotient. The drawback is that there is no canonical...

In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to...

mathematics, an arithmetico-geometric sequence is the result of element-by-element multiplication of the elements of a geometric progression with the corresponding...

not geometrically finite. A hyperbolic manifold is called geometrically finite if it has a finite number of components, each of which is the quotient of...

pseudo-geometric ring if it is Noetherian and universally Japanese (or, which turns out to be the same, if it is Noetherian and all of its quotients by a...

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties...

In abstract algebra, the total quotient ring or total ring of fractions is a construction that generalizes the notion of the field of fractions of an integral...

that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization...

relative version of the Abel map. Categorical quotient, a special case One also needs to assume the geometric fibers are integral schemes; Mumford's example...

Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with...

theorem states that there is an algebraic space that is a geometric and uniform categorical quotient of X by j, which is separated if j is finite. A corollary...

groundbreaking geometric invariant theory (GIT), developed by David Mumford in 1965, which shows that under suitable conditions the quotient indeed exists...

itself) and angles (the cosine of the angle between two vectors is the quotient of their dot product by the product of their lengths). The name "dot product"...