Degeneration of the Leray spectral sequence for certain geometric quotients

We prove that the Leray spectral sequence in rational cohomology for the quotient map $U_{n,d}\to U_{n,d}\mathrm{/}G$ where $U_{n,d}$ is the affine variety of equations for smooth hypersurfaces of degree $d$ in ${\text{PP}}^n(\text{C})$ and $G$ is the general linear group, degenerates at $E_2$.