Fractional Calabi�Yau categories from Landau�Ginzburg models
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Foundation Compositio Mathematica
https://doi.org/10.14231/ag-2018-016
https://doi.org/10.14231/ag-2018-016
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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.
National Science Foundation under Award No.\ DMS-1401446 and the Engineering and Physical Sciences Research Council under Grant EP/N004922/1
National Science Foundation under Award No.\ DMS-1401446 and the Engineering and Physical Sciences Research Council under Grant EP/N004922/1