Self-Duality for Landau--Ginzburg models
  P. Clarke describes mirror symmetry as a duality between Landau--Ginzburg models, so that the dual of an LG model is another LG model. We describe examples in which the underlying space is a total space of a vector bundle on the projective line, and we show that self-duality occurs in precisely two cases: the cotangent bundle and the resolved conifold. 
Brian Callander, Elizabeth Gasparim, Rollo Jenkins, Lino Marcos Silva
math.AG