Remarks on degenerations of hyper-K\"ahler manifolds

  title={Remarks on degenerations of hyper-K\"ahler manifolds},
  author={J'anos Koll'ar and Radu Laza and Giulia Sacc{\`a} and Claire Voisin},
  journal={arXiv: Algebraic Geometry},
Using the Minimal Model Program, any degeneration of K-trivial varieties can be arranged to be in a Kulikov type form, i.e. with trivial relative canonical divisor and mild singularities. In the hyper-K\"ahler setting, we can then deduce a finiteness statement for monodromy acting on $H^2$, once one knows that one component of the central fiber is not uniruled. Independently of this, using deep results from the geometry of hyper-K\"ahler manifolds, we prove that a finite monodromy projective… Expand
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