Algebraic geometry

Geometric quotient

In algebraic geometry, a geometric quotient of an algebraic variety X with the action of an algebraic group G is a morphism of varieties such that (i) For each y in Y, the fiber is an orbit of G.(ii) The topology of Y is the quotient topology: a subset is open if and only if is open.(iii) For any open subset , is an isomorphism. (Here, k is the base field.) The notion appears in geometric invariant theory. (i), (ii) say that Y is an orbit space of X in topology. (iii) may also be phrased as an isomorphism of sheaves . In particular, if X is irreducible, then so is Y and : rational functions on Y may be viewed as invariant rational functions on X (i.e., of X). For example, if H is a closed subgroup of G, then is a geometric quotient. A GIT quotient may or may not be a geometric quotient: but both are categorical quotients, which is unique; in other words, one cannot have both types of quotients (without them being the same). (Wikipedia).

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What is a geometric mean

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN

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How to determine the geometric mean between two numbers

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN

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Learn how to find the geometric mean between two numbers

Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.

From playlist Geometry - GEOMETRIC MEAN

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Write the first five terms of the geometric sequence

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Evaluate the expression of a term of a geometric sequence

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From playlist Sequences

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How to find the first five terms of a geometric sequence

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From playlist Sequences

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From playlist Sequences

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From playlist Series

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Talk by Emile Takahiro Okada (University of Oxford, UK)

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From playlist Seminars: Representation Theory and Number Theory

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From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette

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From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

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From playlist Mathematics

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From playlist Global Noncommutative Geometry Seminar (Americas)

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From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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From playlist Geometry, Groups and Dynamics (GGD) - 2017

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From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)

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Related pages

Geometric invariant theory | Algebraic group | GIT quotient | Topology | Algebraic geometry | Categorical quotient | Algebraic variety