= Geometric invariant theory
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= GIT
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<Geometric invariant theory> constructs algebraic quotients of <group actions> by a <reductive algebraic group> using invariant sections and a chosen <linearization of a line bundle>. An affine quotient is the spectrum of the <polynomial invariant ring>; a projective quotient uses homogeneous invariants and excludes the points where all positive-degree invariants vanish. Stability separates the orbits which give well-behaved <geometric quotient> points.
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