Singularities of Landau-Ginzburg models for complete intersections and derived categories
Abstract
Mirror symmetry predicts that bounded derived category of a smooth Fano variety is equivalent to Fukaya-Seidel category of its Landau-Ginzburg model. It is expected that fibers of Landau-Ginzburg model with ordinary double points correspond to an exceptional collection of a Fano variety. We verify this expectation on a numerical level for Fano complete intersections and Calabi-Yau compactifications of their toric Landau-Ginzburg models of Givental's type.
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