GIT quotient
MATHEMATICAL CONSTRUCTION THAT PRODUCES, GIVEN A REDUCTIVE GROUP G ACTING ON AN EQUIVARIANT INVERTIBLE SHEAF OVER A VARIETY X, A QUOTIENT SCHEME X⫽G AND A MORPHISM FROM AN OPEN SUBSCHEME (OF SEMISTABLE POINTS): Xˢˢ → X⫽G
Geometric invariant theory quotient
In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme X = \operatorname{Spec} A with an action by a group scheme G is the affine scheme \operatorname{Spec}(A^G), the prime spectrum of the ring of invariants of A, and is denoted by X /\!/ G.