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Iskovskikh Seminar
November 28, 2013 15:30, Moscow, Steklov Mathematical Institute, room 540
 


Derived categories and Hodge theory of some Fano 4-folds

Alex Perry

Harvard University

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Abstract: I will talk about Fano 4-folds of Picard number 1, degree 10, and index 2. They are similar to cubic 4-folds in many respects. In particular, the derived category of such a 4-fold $X$ admits a semiorthogonal decomposition into an exceptional sequence and an interesting 2-Calabi–Yau category $A_X$. I will discuss how rationality of $X$ relates to the condition that $A_X$ is equivalent to the derived category of a K3 surface, and also connections between $A_X$ and the Hodge theory of $X$.

Language: English

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