Geometric realizations of non-symplectic involutions on the Hilbert square of a K3 surface

We give new examples of geometric constructions of non-natural non-symplectic involutions of IHS manifolds whose existence is guaranteed by previous results of Bossière-Cattaneo-Nieper-Wiesskirchen-Sarti in arXiv:1410.8387 and Bossiére-Camere-Sarti in arXiv:1402.5154.