Under the free-action assumption on the stable locus, components of the torus fixed-point locus on a GIT quotient are GIT quotients of linear subspaces by Levi subgroups.
Ness, A stratification of the null cone via the moment map (with an appendix by D
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Torus Actions on Quotients of Affine Spaces
Under the free-action assumption on the stable locus, components of the torus fixed-point locus on a GIT quotient are GIT quotients of linear subspaces by Levi subgroups.