Fractional Calabi-Yau Categories from Landau-Ginzburg Models

David Favero; Tyler L. Kelly

Fractional Calabi-Yau Categories from Landau-Ginzburg Models

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

Fractional Calabi-Yau Categories from Landau-Ginzburg Models

David Favero , Tyler L. Kelly This is my paper

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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