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Title:
Derived categories of varieties with rational singularities
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Abstract:
Given a resolution of rational singularities Y -> X, there are old Bondal-Orlov conjectures relating derived categories of coherent sheaves on Y and on X. I will explain what is known about these conjectures and prove that the image of the pushforward map generates the derived category of X. The proof boils down to verifying that under some conditions, fibers of the resolution are O-acyclic, which is based on a Hodge theory argument. This is joint work with Mirko Mauri.
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