  To better understand vortex pinning in thin superconducting slabs, we study
the interaction of a single fluctuating vortex filament with a curved line
defect in (1+1) dimensions. This problem is also relevant to the interaction of
scratches with wandering step edges in vicinal surfaces. The equilibrium
probability density for a fluctuating line attracted to a particular fixed
defect trajectory is derived analytically by mapping the problem to a straight
line defect in the presence of a space and time-varying external tilt field.
The consequences of both rapid and slow changes in the frozen defect
trajectory, as well as finite size effects are discussed. A sudden change in
the defect direction leads to a delocalization transition, accompanied by a
divergence in the trapping length, near a critical angle.
