  We study deformations of Landau-Ginzburg D-branes corresponding to obstructed
rational curves on Calabi-Yau threefolds. We determine D-brane moduli spaces
and D-brane superpotentials by evaluating higher products up to homotopy in the
Landau-Ginzburg orbifold category. For concreteness we work out the details for
lines on a perturbed Fermat quintic. In this case we show that our results
reproduce the local analytic structure of the Hilbert scheme of curves on the
threefold.
