EPW cubes are six-dimensional projective hyper-Kähler varieties constructed by Iliev, Kapustka, Kapustka, and Ranestad. Their construction and properties share many similarities with the double EPW sextics introduced by O’Grady. Both double EPW sextics and EPW cubes belong to the few known families of hyper-Kähler varieties for which one can give a geometric description of a general element in the moduli space. Moreover, both admit an anti-symplectic involution whose fixed locus is a Lagrangian <a href="http://submanifold.
In » target= »_blank » title= »submanifold.
In »>submanifold.
In the first part of the talk, we will review the notion of hyper-Kähler varieties and their cohomology rings. We will then talk about EPW cubes, along with their properties, and present the rigidity result concerning the fixed locus of the anti-symplectic <a href="http://involution. 
In » target= »_blank » title= »involution. 
In »>involution. 
In the second part, we will describe the degeneration techniques developed by Flapan, Macrì, O’Grady, and Saccà that are used to study the geometry of the fixed <a href="http://locus.

https://indico.math.cnrs.fr/event/14994/ » target= »_blank » title= »locus.

https://indico.math.cnrs.fr/event/14994/ »>locus.

https://indico.math.cnrs.fr/event/14994/