Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

@article{Harvey2010CharacterizingPS,
  title={Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces},
  author={David Harvey and Brendan Hassett and Yuri Tschinkel},
  journal={Communications on Pure and Applied Mathematics},
  year={2010},
  volume={65}
}
We seek to characterize homology classes of Lagrangian projective spaces embedded in irreducible holomorphic‐symplectic manifolds, up to the action of the monodromy group. This paper addresses the case of manifolds deformation‐equivalent to the Hilbert scheme of length‐3 subschemes of a K3 surface. The class of the projective space in the cohomology ring has prescribed intersection properties, which translate into Diophantine equations. Possible homology classes correspond to integral points on… 
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