28 jun 2017 -- 14:30
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
The key tool for understanding degenerations of K3 surfaces is the Kulikov-Persson-Pinkham theorem (a semi-stable degeneration of K3 surfaces can be modified to have trivial canonical bundle). Recent advances in the minimal model program (with essential further contributions from Fujino) give an analogous result on higher dimensional hyperkähler 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 hyperkähler constructions, and some results on the dual complex of a semi-stable degeneration of hyperkählers). This is a report on joint work with J. Kollár, G. Saccà, and C. Voisin.