Non-symplectic involutions on manifolds of K3^{[n]}-type

Thursday, 14 February, 2019

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We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a K3 surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and anti-invariant lattice for the action of the involution on cohomology, and explicitly describe the lattices in the cases where the invariant has small rank. We also give a modular description of all d-dimensional families of manifolds of K3^{[n]}-type with a non-symplectic involution for d\geq 19 and n\leq 5, and provide examples arising as moduli spaces of twisted sheaves on a K3 surface.


Chiara Camere
Alberto Cattaneo
Andrea Cattaneo