If I have an equivariant morphism $F:X\rightarrow Y$ and I want to prove that if the tangent map is onto over every point of $X$. Where $X$ and $Y$ are affine varieties invariants by the action of $GL_3$. I know the subset $A=\{x\in X ;\ \ \mbox{the tangent map is not onto on } x \}$ is closed.
Supposing that $A$ is not empty; if $A$ was invariant then it contents a closed orbit, by the other side I know that the tangent map is onto on a representative of that closed orbit (in this particular case), and I would have a contradiction. Then I have that $A=\emptyset$ . How can I prove that $A$ is invariant?