Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomialy 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. Is that true that the polynomial functions' $G$-invariants separate the orbits?

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?

Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomialy 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. Is that true that the $G$-invariants polynomial functions separate the orbits?

Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomialy 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. Is that true that the polynomial functions' $G$-invariants separate the orbits?