
Relative geometric invariant theory is an invariant theory for equivariant projective morphisms between algebraic varieties endowed with an action of a reductive linear algebraic group. We will give brief accounts of the basic results of relative geometric invariant theory and present alternative proofs for recent results obtained by Halle, Hulek, and Zhang on the variation of quotients in relative geometric invariant theory.
Hilbert-Mumford criterion, Geometric invariant theory, Group actions on varieties or schemes (quotients), quotient, Stacks and moduli problems, semistability, equivariant morphism, variation of quotients and moduli spaces, relative moduli space
Hilbert-Mumford criterion, Geometric invariant theory, Group actions on varieties or schemes (quotients), quotient, Stacks and moduli problems, semistability, equivariant morphism, variation of quotients and moduli spaces, relative moduli space
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