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Title:
Crepant Categorical Resolutions and a Toric Orlov Theorem
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Abstract:
Desingularizing a variety is, of course, not unique. For example, there can be many crepant resolutions of a given space. However, in their pioneering work on derived categories, Bondal and Orlov conjectured that all such resolutions have equivalent derived categories. In this way, categorically resolving singularities may have some nicer properties that classical resolutions. I will discuss how a toric version of Orlov's theorem provides a method of obtaining categorical crepant resolutions can be given explicit geometric realizations as Landau-Ginzburg models. We will focus on some motivating examples such as Kuznetsov's categorical crepant resolution of the K3 category inside a singular cubic 4-fold. This is joint work with T. Kelly.
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