If $X$ is a smooth projective variety of dimension $r$ over $\mathbf{C}$ then the Leray spectral sequence of the (ordered) configuration space $F^n X$ of $n$ points on $X$ including into $X^n$ has only $d_{2r}$ nonvanishing.
Burt Totaro, "Configuration space of algebraic varieties", Topology, vol. 35, no. 4, pp. 1057–1067, Oct. 1996.