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 semiorthogonal decompositions containing (fractional) Calabi-Yau categories.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 596-649 |
| Number of pages | 54 |
| Journal | Algebraic Geometry |
| Volume | 5 |
| Issue number | 5 |
| DOIs | |
| State | Published - Sep 1 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© Foundation Compositio Mathematica 2018.
Keywords
- Calabi-Yau categories
- Derived categories
- Landau-Ginzburg models
- Matrix factorizations
- Toric varieties
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