Fractional Calabi-Yau Categories from Landau-Ginzburg Models
David Favero, Tyler L. Kelly
TL;DR
This paper establishes criteria for Serre functors in gauged Landau-Ginzburg models, enabling the construction of fractional Calabi-Yau subcategories and providing a geometric framework for crepant resolutions, with explicit toric examples.
Contribution
It introduces a general theorem for the existence of fractional Calabi-Yau subcategories in gauged Landau-Ginzburg models and extends existing results with new semi-orthogonal decompositions.
Findings
Criteria for Serre functors in gauged Landau-Ginzburg models
Construction of fractional Calabi-Yau subcategories
New examples of semi-orthogonal decompositions
Abstract
We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged Landau-Ginzburg model and a geometric context for crepant categorical resolutions. We explicitly describe our framework in the toric setting. As a consequence, we generalize several theorems and examples of Orlov and Kuznetsov, ending with new examples of semi-orthogonal decompositions containing (fractional) Calabi-Yau categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons