2023/11/22 by Greb, Daniel, Schwald, Martin
#14C05 #14C30 #14J28 #14J42 #32G07 #32G13 #32G20 #32L25 #53C28 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.13420
We answer a question posed independently by Fels-Huckleberry-Wolf and Looijenga concerning the geometric meaning of small deformations of twistor cycles in the K3 period domain. These are shown to induce complex-hyperkähler metrics on members of the families via Penrose's Non-linear Graviton construction. On the way to proving this result, we construct a Hausdorff fine moduli space for families of marked K3 surfaces over smooth rational curves in the K3 period domain. Over an open subset containing all twistor cycles we construct a family of such families, which is a universal small deformation for every twistor family. Whenever possible, we extend the results to higher-dimensional irreducible holomorphic-symplectic manifolds.