2025/09/25 by Peize Liu, Liu, Peize
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2509.21454
We study the Kuznetsov component of a smooth cubic fivefold. Using a quadric surface fibration, we construct a family of Serre-invariant Bridgeland stability conditions on the Kuznetsov component. For every non-zero numerical class, we prove that the associated Bridgeland moduli space on the Kuznetsov component is non-empty. When the cubic fivefold is general and the numerical class is primitive, the moduli space contains a smooth locus, on which the restriction to a general hyperplane section preserves stability. Consequently, we obtain Lagrangian immersions into hyper-Kähler varieties arising as moduli spaces on the Kuznetsov component of cubic fourfolds, extending the work of Li-Lin-Pertusi-Zhao on cubic 3-folds. As an example, we recover the geometric construction of Illiev-Manivel, which realizes the Fano surface of planes of the cubic fivefold as a Lagrangian subvariety in a hyper-Kähler fourfold.