  The line bundle mean curvature flow is a complex analogue of the mean
curvature flow for Lagrangian graphs, with fixed points solving the deformed
Hermitian-Yang-Mills equation. In this paper we construct two distinct examples
of singularities along the flow. First, we find a finite time singularity,
ruling out long time existence of the flow in general. Next we show long time
existence of the flow with a Calabi symmetry assumption on the blowup of
$\mathbb P^n$, $n\geq 3$, if one assumes supercritical phase. Using this, we
find an example where a singularity occurs at infinite time along the
destabilizing subvariety in the semi-stable case.
