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Fractional Calabi-Yau Categories from Landau-Ginzburg Models

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arxiv 1610.04918 v3 pith:HZ2TU2IX submitted 2016-10-16 math.AG

David Favero , Tyler L. Kelly This is my paper · ORCID
classification math.AG
keywords calabi-yaufractionallandau-ginzburgcategoriesexamplesexistencegaugedmodel
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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.

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  1. Notes on the Kuznetsov component of cubic sevenfolds

    math.AG 2026-07 accept novelty 7.0 of 10

    For smooth cubic sevenfolds, the Kuznetsov component embeds into the derived category of Clifford modules on P^4; for a general nodal-line cubic, its Kuznetsov component admits an explicit weakly crepant categorical r...

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