Geometric quotient
id:
geometric-quotient-287-1213840
title:
Geometric quotient
text:
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 such that 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 O Y ≃ π ∗ . In particular, if X is irreducible, then so is Y and k = k G : rational functions on Y may be viewed as invariant rational functions on X. For example, if H is a closed
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wiki
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encyclopedia
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original url:
https://en.wikipedia.org/wiki/Geometric_quotient
date created:
date modified:
2024-04-03T15:38:50Z
main entity:
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13
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