The paper constructs explicit non-symplectic involutions on Hilbert squares of K3 surfaces, including a non-natural involution with invariant lattice <2>⊕<-2>.
Non-natural non-symplectic involutions on symplectic manifolds of K3^{[2]}-type
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abstract
We study non-symplectic involutions on irreducible symplectic manifolds of K3^{[2]}-type with 19 parameters, which is the second largest possible. We classify the conjugacy classes of cohomological representations into four different types and show that there are at most five deformation types, two of which are given by natural involutions and their flops. Next, we give a geometric realisation of one of the new types using moduli spaces of sheaves on K3 surfaces. The geometry of the manifold and the new involution is described in detail.
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Geometric realizations of non-symplectic involutions on the Hilbert square of a K3 surface
The paper constructs explicit non-symplectic involutions on Hilbert squares of K3 surfaces, including a non-natural involution with invariant lattice <2>⊕<-2>.