The mirror symmetry predicts that the bounded derived category of a smooth Fano variety is equivalent to the Fukaya–Seidel category of its Landau–Ginzburg model. It is expected that the fibers of Landau–Ginzburg model with ordinary double points correspond to an exceptional collection of a Fano variety. We verify this expectation at a numerical level for Fano complete intersections and Calabi–Yau compactifications of their toric Landau–Ginzburg models of Givental’s type.
V.V. Przyjalkowski (Sun,) studied this question.