Fractional Calabi-Yau categories via Landau-Ginzburg models

David Favero, Tyler Kelly

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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.
Original languageEnglish
Pages (from-to)596-649
Number of pages54
JournalAlgebraic Geometry
Issue number5
Publication statusPublished - 1 Sept 2018


  • Calabi-Yau catagories
  • Landau-Ginzburg models
  • derived catagories
  • matrix factorizations
  • toric varieties


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