  We show the local rigidity of complex hyperbolic lattices in classical
Hermitian semisimple Lie groups, $SU(np,p), Sp(2n+2,\mathbb R), SO^*(2n+2),
SO(2n,2)$. This reproves or generalizes some results in \cite{GM, KKP,
Klingler-inv, Pozzetti}.
