Proof of Kulikov's Theorem on Degenerations of K3-surfaces via the Minimal Model Program

In 1977 V. S. Kulikov showed that a semi-stable degeneration of K3-surfaces, such that all irreducible components of the special fiber are algebraic, after a series of birational transformations can be arranged into a semi-stable degeneration with relatively trivial canonical bundle. In his recent paper, J. Jiménez proposed another proof of this theorem based on the minimal model program. We will discuss this proof; moreover, I will try to explain why this proof implies that one cannot run the minimal model program for an arbitrary complex manifold.