Derived Equivalence and the Picard Variety

Derived Equivalence and the Picard Variety

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Christian Schnell, University of Illinois at Chicago (UIC)
Fine Hall 322

I will explain a result, joint with Mihnea Popa, saying that if two smooth projective varieties have equivalent derived categories of coherent sheaves, then their Picard varieties are isogeneous; in particular the number of independent holomorphic one-forms is a derived invariant. A consequence of this is that derived equivalent threefolds have the same Hodge numbers.