# 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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