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Abstract des Vortrages von Marcelleo Bernardara

Homological projective duality for determinantal varieties

In this talk I will present joint results with M.Bolognesi and D.Faenzi. Using homological projective duality for projective bundles and categorical resolution of singularities constructed by Buchweitz, Leuschke and Van den Bergh, we show homological projective duality for generalized determinantal varieties. As an application, we find derived equivalent (and birational) CY-manifolds and we show that the following question of A.Bondal: "for any variety X, does it exist a Fano variety Y and a full and faithful fucntor D(X) \to D(Y)?" has a positive answer in many cases, for example when X is a smooth plane curve.