Sukhendu Mehrotra, University of Massachusetts, Amherst

A Categorial Torelli Theorem for Cubic Threefolds

It is a famous theorem of Clemens-Griffiths and Tyurin that a cubic threefold is determined by its intermediate Jacobian. We discuss a categorical version of this theorem, namely, that a cubic threefold is determined by a semi-orthogonal component of its derived category. Our approach is to construct an interesting Bridgeland stability condition on this component and recover the intermediate jacobian as a moduli space of stable objects. This is joint work with Bernardara, Macri and Stellari.

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