Recent developments by Druel, Greb-Guenancia-Kebekus, Horing-Peternell have led to the formulation of a decomposition theorem for singular (klt) projective varieties with numerical trivial canonical class. Irreducible symplectic varieties are one the building blocks provided by this theorem, and the singular analogue of irreducible hyper-Kähler manifolds. In this talk I will show that moduli spaces of Bridgeland stable objects on the Kuznetsov component of a cubic fourfold with respect to a generic stability condition are always projective irreducible symplectic varieties. I will rely on the recent work of Bayer-Lahoz-Macri-Neuer-Perry-Stellari, which, ending a long series of results by several authors, proved the analogue statement in the smooth case.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
