Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomially on $\mathbb{C}^n$. Suppose that the quotient exists as an analytical geometric quotient, i.e., $\mathbb{C}^n/G$ is a smooth analytic manifold and the quotient map is analytic. Do $G$-invariants separate the orbits?
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$\begingroup$ I would recommend trying a more specific title for the post; would "Smooth quotients and separation of orbits" be reasonable? Tags already tell us we're talking about GIT. $\endgroup$– Marco GollaCommented Oct 7, 2016 at 8:21
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$\begingroup$ Done. Thx for the advice. $\endgroup$– YoyoCommented Oct 7, 2016 at 8:23
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