Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

Understand

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-three 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 an explicit elliptic curve; our proof entails showing that the only such point is two-torsion.