  We give a geometric interpretation for D-branes in the c=1 string theory. The
geometric description is provided by complex curves which arise in both CFT and
matrix model formulations. On the CFT side the complex curve appears from the
partition function on the disk with Neumann boundary conditions on the
Liouville field (FZZ brane). In the matrix model formulation the curve is
associated with the profile of the Fermi sea of free fermions. These two curves
are not the same. The latter can be seen as a certain reduction of the former.
In particular, it describes only (m,1) ZZ branes, whereas the curve coming from
the FZZ partition function encompasses all (m,n) branes. In fact, one can
construct a set of reductions, one for each fixed n. But only the first one has
a physical interpretation in the corresponding matrix model. Since in the
linear dilaton background the singularities associated with the ZZ branes
degenerate, we study the c=1 matrix model perturbed by a tachyon potential
where the degeneracy disappears. From the curve of the perturbed model we give
a prediction how D-branes flow with the perturbation and derive the two-point
bulk correlation function on the disk with the FZZ boundary conditions.
