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

TL;DR

This paper presents new geometric constructions of non-symplectic involutions on the Hilbert square of a K3 surface, expanding the known examples of such involutions in irreducible holomorphic symplectic manifolds.

Contribution

It introduces novel geometric methods to realize non-symplectic involutions on Hilbert squares of K3 surfaces, building on prior theoretical existence results.

Findings

New explicit geometric examples of non-symplectic involutions

Extensions of previous existence results to concrete constructions

Enhanced understanding of involution symmetries in IHS manifolds

Abstract

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