Some remarks on degenerations of Hyper-Kaehler Manifolds

Abstract: The key tool for understanding degenerations of K3 surfaces is the Kulikov-Person-Pinkham theorem (a semi-stable degeneration of K3 surfaces can be normalized to have trivial relative canonical bundle). Recent progress in MMP (with essential further contributions from Fujino) give an analogous result on higher dimensional HK manifolds. In this talk, I will explore some geometric consequences of this result (e.g. a simplification of some proofs of deformation type for certain HK constructions, and some results on the dual complex of a semi-stable degeneration of HKs).

This is a report on work in progress with J. Kollár, G. Sacca, and C. Voisin