  We continue the study the Dolbeault dga of the formal neighborhood of an
arbitary closed embedding of complex manifolds previously defined by the author
in \cite{DolbeaultDGA}. The special case of the diagonal embedding has been
studied in \cite{Diagonal}. We describe the Dolbeault dga explicitly in terms
of the formal differential geometry of the embedding. Moreover, we show that
the Dolbeault dga is the completed Chevalley-Eilenberg dga an
$L_\infty$-algebroid structure on the shifted normal bundle of the submanifold.
This generlizes the result of Kapranov on the diagonal embedding and Atiyah
class.
