Algebraic Geometry Seminar

A global Torelli theorem does not hold for Calabi–Yau 3-folds: the best counterexample, due independently to Ottem and Rennemo and to Borisov, Caldararu, and Perry, gives pairs of CY3s in the same deformation family that have equivalent derived categories of coherent sheaves, hence isomorphic polarized Hodge structures on H^3(X,Z), but are not birationl. One might then ask whether a derived Torelli theorem holds. I will discuss an example of Aspinwall, Morrison, and Szendrői, which was expected to provide a counterexample; it turns out not to, but fits into the whole picture in a surprising way. This is joint work with Ben Tighe, arXiv:2407.11176.