Singularities of Landau-Ginzburg models for complete intersections and derived categories
Victor Przyjalkowski
TL;DR
This paper investigates the relationship between Landau-Ginzburg models and derived categories of Fano varieties, confirming numerical predictions about singular fibers and exceptional collections in specific cases.
Contribution
It provides a numerical verification of the mirror symmetry prediction relating Landau-Ginzburg models and derived categories for Fano complete intersections.
Findings
Fibers with ordinary double points correspond to exceptional collections.
Numerical verification for Fano complete intersections.
Supports mirror symmetry conjectures in specific cases.
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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