  For a group $G$ that is a limit group over Droms RAAGs such that $G$ has
trivial center, we show that $\Sigma^1(G) = \emptyset = \Sigma^1(G,
\mathbb{Q})$. For a group $H$ that is a finitely presented residually Droms
RAAG we calculate $\Sigma^1(H)$ and $\Sigma^2(H)_{dis}$. In addition, we obtain
a necessary condition for $[\chi]$ to belong to $\Sigma^n(H)$.
