  Large classes of AdS$_p$ supergravity backgrounds describing the IR dynamics
of $p$-branes wrapped on a Riemann surface are determined by a solution to the
Liouville equation. The regular solutions of this equation lead to the
well-known wrapped brane supergravity solutions associated with the constant
curvature metric on a compact Riemann surface. We show that some singular
solutions of the Liouville equation have a physical interpretation as explicit
point-like brane sources on the Riemann surface. We uncover the details of this
picture by focusing on $\mathcal{N}=1$ theories of class $\mathcal{S}$ arising
from M5-branes on a punctured Riemann surface. We present explicit AdS$_5$
solutions dual to these SCFTs and check the holographic duality by showing the
non-trivial agreement of 't Hooft anomalies.
