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The noncommutative K3 surface of a cubic fourfold and hyperkaehler geometry

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Laura Pertusi
Università degli Studi di Milano/MPIM
Tue, 2019-04-09 14:00 - 15:00
MPIM Lecture Hall

In 2008 Kuznetsov proved that the bounded derived category of a cubic fourfold Y has a semiorthogonal decomposition whose
non-trivial component Ku(Y) is a K3 subcategory. More recently, Bayer, Lahoz, Macri` and Stellari constructed Bridgeland
stability conditions on Ku(Y), making possible to study moduli spaces of semistable objects in this component.

The aim of this talk is to explain the modular interpretation of some hyperkaehler manifolds, classically associated to Y.

As an application, we reprove the categorical version of Torelli theorem for cubic fourfolds and we study the period point
of the hyperkaehler eightfold constructed out of twisted cubic curves in Y. This is the content of a joint work with Chunyi Li
and Xiaolei Zhao.

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