Derived categories of Fano varieties of degree 10

Alex Perry (Harvard)

We will discuss the derived categories of Fano varieties of Picard number 1, degree 10, and coindex 3. The derived category of such a variety X admits a semiorthogonal decomposition into an exceptional sequence of vector bundles and an interesting category A_X. In the 4-dimensional case, we will describe: (1) a locus in the moduli space where X is rational and A_X is equivalent to the derived category of a K3 surface; (2) a locus where X is birational to a cubic fourfold Y and A_X is equivalent to an analogous category associated to Y. For "hyperelliptic" X, we will also describe a relation between A_X and the category attached to a degree 10 variety of one dimension less. This is joint work with Alexander Kuznetsov.

Tuesday, October 7th, at 4:00pm in HBH 227

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