Obstructed D-Branes in Landau-Ginzburg Orbifolds
  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. 
Sujay K. Ashok, Eleonora Dell'Aquila, Duiliu-Emanuel Diaconescu,   Bogdan Florea