  We investigate a complex curve in the $c=1$ string theory which provides a
geometric interpretation for different kinds of D-branes. The curve is
constructed for a theory perturbed by a tachyon potential using its matrix
model formulation. The perturbation removes the degeneracy of the non-perturbed
curve and allows to identify its singularities with ZZ branes. Also, using the
constructed curve, we find non-perturbative corrections to the free energy and
elucidate their CFT origin.
