📝 SummarXiv

Abstract

We study the Kuznetsov component of cubic fivefolds via their quadric fibration model. We construct a family of Serre-invariant Bridgeland stability conditions on the Kuznetsov component and establish the non-emptiness of all moduli spaces of stable objects. As an application, we identify the lowest-dimensional moduli with the Fano surface of planes of the cubic fivefold, and recover a classical result of its Lagrangian immersion into a hyper-K\"ahler manifold.